Is there any mention in the Islamic texts of a minimum period that sinners among the people of Tawheed will spend in Hell?
Question

What is the minimum duration for a muslim in Jahannam advised in Quran and authentic Hadith?
Praise be to Allah.Firstly: 
With regard to anyone among the people of Tawheed who enters Hell, his punishment and length of stay therein will be commensurate with the level of his sin, then he will be brought out of it. Some of them will be brought out of it by the intercession of the Prophets; some will be brought out of it by the intercession of the righteous; and some of them will be brought out of it by the mercy of the Lord of the Worlds, without intercession from anyone. 
Please see the answer to question no.  21672 
Muslim (2845) narrated from Samurah (may Allah be pleased with him) that the Prophet of Allah (blessings and peace of Allah be upon him) said: “There are some whom the Fire will seize up to the ankles, and some whom it will seize up to the waist, and some whom it will seize up to the neck.”  
Al-Haafiz (may Allah have mercy on him) said: 
It may be that this was narrated concerning those among the people of Tawheed who enter the Fire, and the circumstances of their punishment will vary according to their deeds. As for the disbelievers, they will be fully immersed in the Fire.
End quote from Fath al-Baari (11/394) 
Al-Haafiz Ibn Rajab (may Allah have mercy on him) said: 
Similarly the punishment of the sinners among the people of Tawheed in Hell will vary according to their deeds. The punishment of those who committed major sins will not be like the punishment of those who committed minor sins, and the punishment of some of them may be reduced by virtue of other good deeds that they did, or for other reasons as Allah wills. Hence some of them will die in Hell.
End quote from at-Takhweef min an-Naar (p. 182) 
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 
The sinners among the Muslims are of three types: those whom Allah will forgive and they will not enter the Fire at all; another group who will enter the Fire and be punished according to their sins, then brought out; and a third group who will enter the fire and be punished, but intercession will be made for them and they will be brought out of the Fire before they have received in full the punishment that they deserve.
Fataawa Noor ‘ala ad-Darb (4/2) 
Secondly: 
With regard to the intensity of punishment, no one knows how severe it will be or how long it will last except Allah. In that regard they will vary according to their sins. 
No one knows the minimum duration of the period that these sinners will spend in Hell, just as no one knows the maximum duration thereof. But what Ahl as-Sunnah are unanimously agreed upon is that they will be punished therein as Allah wills that they should be punished, each according to his sins and transgressions, then Allah will admit them to Paradise by His mercy.
Shaykh ‘Abd al-‘Azeez ar-Raajihi (may Allah preserve him) said: 
There are numerous reports from the Prophet (blessings and peace of Allah be upon him) which state that a number of those among the believers and people of Tawheed who commit major sins will enter Hell; they will enter it because of major sins from which they had not repented before they died. Some will enter Hell because they died without having repented from zina; others will enter it because they died without having repented from riba, or disobedience towards parents, or severing ties of kinship, or backbiting, or supporting falsehood, or bearing false witness. Some of them will be pardoned and others will enter Hell and be punished. But they will vary in terms of their coming out of Hell. Some of them will remain there for a long time and others will remain there for a short time, according to their sins and deeds, then they will be brought out by virtue of intercession.
Once all the sinners among the people of Tawheed have been brought out of Hell and there are none of them left, the Fire will fold in upon the disbelievers of all types. 
The believers who are brought out will be thrown into the River of life, and they will grow like seeds in the silt carried by a flood. Then when they have been purified and cleansed, permission will be given to them to enter Paradise. End quote.
 
We do not know of any report that specifies the duration of the Muslim sinners’ stay in Hell apart from two hadeeths, both of which are munkar (odd) and are not saheeh (sound). 
The first of them was narrated by Ibn Abi Haatim in his Tafseer, as is stated in Tafseer Ibn Katheer (4/425) via Miskeen Abu Faatimah: al-Yamaan ibn Yazeed told me, from Muhammad ibn Himyar, from Muhammad ibn ‘Ali, from his father, from his grandfather, that the Prophet (blessings and peace of Allah be upon him and his family) said: “Those who commit major sins, among the people of Tawheed of all nations, if they die whilst still committing their sins, without regretting it or repenting – whoever among them enters the Fire, through the first gate of Hell, their eyes will not turn blue and their faces will not turn black, and they will not be paired with the devils, tied up in chains, or be given boiling water to drink or clothed in (garments of) pitch from the Fire. Allah will forbid their bodies to abide therein forever because of Tawheed, and He will forbid their faces to the Fire because of their prostration. Some of them will be seized by the Fire up to their feet; some of them will be seized by the Fire up to the waist and some of them will be seized by the fire up to the neck, according to their sins and actions. Some of them will remain there for one month, then be brought out; some will remain there for one year, then be brought out of it; those who remain there for the longest time will remain as long as this world existed, from the day it was created until it ceased to be…” 
This is how it was narrated by al-Haafiz Ibn Rajab (may Allah have mercy on him) in at-Takhweef min an-Naar (p. 259), then he said: It was narrated by Ibn Abi Haatim and others; and it was narrated at length by al-Isma‘eeli. Ad-Daaraqutni (may Allah have mercy on him) said in Kitaab al-Mukhtalaq: It is a munkar (odd) hadeeth. Al-Yamaan is unknown, Miskeen is da‘eef (weak), and I do not know of Muhammad ibn Himyar except from this hadeeth. End quote. 
The second hadith was narrated by al-Hakeem at-Tirmidhi in Nawaadir al-Usool (2/36) from Abu Hurayrah (may Allah be pleased with him) in a marfoo‘ report: “Rather intercession on the Day of Resurrection will be for those among my ummah who committed major sins then died in that state, and they will be in the first gate of Hell. Their faces will not turn black and their eyes will not turn blue; they will not be tied up in chains and they will not be paired with the devils. They will not be struck with hooked rods of iron or thrown into the depths of Hell. Some of them will remain therein for one hour, then be brought out; some will remain therein for one day, then be brought out; some of them will remain therein for one month, then be brought out; and some of them will remain therein for one year, then be brought out. Those who stay the longest therein will stay for as long as this world existed, from the day it was created until the day when it ceased to be, which is seven thousand years…” 
This was quoted by al-Albaani in ad-Da‘eefah (5381). He said: It is mawdoo‘ (fabricated) 
For more information, please see the answer to questions no. 26792 and 27075 
And Allah knows best.