The difference between mercy that is created and mercy that is a divine attribute
Question

In some places, some say that Allah is 'INFINITELY' merciful. Now, as we know, Rasul (S) said that, Allah created Rahmah and kept 99 protions for him, doesn't it make the mercy of Allah "Finite"? It seems that It's something created, which is in a Finite amount, 100 portions in total. Also, disbelievers won't get it in the judgement day. So then, it seems it is also reserved for a Finite audience.
And if He is truly Infinite in Mercy, then have I done any sin, as I am doubtful and not understanding about this matter?
Praise be to Allah.Firstly: the mercy of ALlah is of two types
The mercy of Allah is of two types:
The first type is an attribute of the Essence of Allah, may He be exalted. This is not created and it is infinite, for He is the Most Gracious (ar-Rahman), the Most Merciful (ar-Rahim). {And your Lord is the Forgiving, full of mercy} [al-Kahf 18:58].
The second type is created mercy, which is composed of one hundred parts of which Allah sent down one in this world, and He has kept the other ninety-nine parts by which He will show mercy to His slaves on the Day of Resurrection.
Al-Bukhari (6469) narrated that Abu Hurayrah (may Allah be pleased with him) said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Indeed Allah created mercy, on the day He created it, in one hundred parts. Then He kept ninety-nine parts of it with Him and sent one part for all of His creation. If the disbeliever knew of all that there is with Allah of mercy, he would never despair of Paradise, and if the believer knew of all that there is with Allah of punishment, he would never feel safe from the Fire.”
Muslim (2725) narrated it as follows: “Indeed, Allah has one hundred parts of mercy, of which He sent one part to be shared between the jinn, humankind, the animals and the vermin. By virtue of it they show compassion to one another and show mercy to one another, and by virtue of it the wild animal shows compassion to its offspring. And Allah has kept behind ninety-nine parts of mercy, by which He will show mercy to His slaves on the Day of Resurrection.”
In Fatawa al-Lajnah ad-Da’imah (2/400) it says: The Prophet (blessings and peace of Allah be upon him) said: “Indeed Allah created, on the day He created the heavens and the earth, one hundred parts of mercy…” What is meant by the mercy that Allah created? Is it the divine attribute – exalted be Allah above that – or is it mercy that was created and is only for this ummah, and the divine attribute is something else?
Answer: The mercy that is mentioned in the hadith is created mercy. Allah created one hundred parts of mercy, of which He sent down one part, by virtue of which people show mercy towards one another. And He has kept with him ninety-nine parts of mercy for the Day of Resurrection.
This mercy is something other than the divine attribute of mercy, for the attributes of Allah are not created; they are attributes of His essence, and Allah, with His attributes, is the Creator and is not created. End quote.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: “Send down one part of Your mercy”– mercy is of two types:

That mercy which is an attribute of Allah. This is not created and is not separate from the Essence of Allah, may He be glorified and exalted, as He says (interpretation of the meaning: {And your Lord is the Forgiving, full of mercy} [al-Kahf 18:58]. Therefore He cannot be asked to send down this type of mercy.
Mercy that is created, and is one of the impacts of Allah’s mercy, so it is called mercy, as Allah, may He be exalted, says of Paradise in the hadith qudsi: “You are My mercy; by means of you I will bestow My mercy on whomever I will.”(Majmu‘ al-Fatawa 8/430).

Secondly: The disbelievers receive mercy in this world
The disbelievers receive mercy in this world, hence Allah gives them good health, wealth and children, and He sent the Messengers to them and sent down the Books to them. But in the hereafter, He will deal with them according to His justice, so He will cause them to abide forever in the fire of Hell.
Because the disbeliever has shown stubbornness and rejected his Lord and Creator, he is not deserving of mercy.
Ibn al-Jawzi (may Allah have mercy on him) said: One of the signs of Allah’s mercy is His sending of the Messengers and giving the sinners respite. If the disbeliever denies Him, then he is regarded as stubborn, so he is not deserving of mercy. End quote from Kashf al-Mushkil (1/94).
If the disbeliever, despite his disbelief and stubbornness, were admitted to Paradise like the believer, that would be contrary to justice. Hence Allah, may He be exalted, says (interpretation of the meaning):
{Or do those who commit evils think We will make them like those who have believed and done righteous deeds - [make them] equal in their life and their death? Evil is that which they judge} [al-Jathiyah 45:21]
{Or should we treat those who believe and do righteous deeds like corrupters in the land? Or should We treat those who fear Allah like the wicked?} [Sad 38:28]
{Then will We treat the Muslims like the criminals?
What is [the matter] with you? How do you judge?} [al-Qalam 68:35-36].
Allah, may He be glorified, is merciful and just; His mercy does not mean that He will not punish those who deserve to be punished, because that is what is dictated by His justice and also His wisdom.
See also the answer to question no. 211871 .
And Allah knows best.