Holding the vessel in the left hand and supporting it with the right hand when drinking
Question

                If your right hand is occupied when eating and you want to drink some water, is it permissible to hold the cup in your left hand and to support it with the right hand when drinking? How did the Prophet (blessings and peace of Allah be upon him) drink whilst eating?.
Praise be to Allah.
    It is proven in the Sunnah 
    that we are instructed to eat and drink with the right hand, and we are 
    forbidden to do that with the left hand. It was narrated from Ibn ‘Umar (may 
    Allah be pleased with him) that the Messenger of Allah (blessings and peace 
    of Allah be upon him) said: “When one of you eats, let him eat with his 
    right hand, and when he drinks, let him drink with his right hand, for the 
    shaytaan eats with his left hand and drinks with his left hand.”

    Narrated by Muslim, 2020

    It was narrated from Jaabir 
    ibn ‘Abdullah (may Allah be pleased with him) that the Messenger of Allah 
    (blessings and peace of Allah be upon him) said: “Do not eat with the left 
    hand, for the Shaytaan eats with the left hand.”

    Narrated by Muslim, 2019.

    If a person needs to use both 
    hands, there is nothing wrong with that because of the report which says 
    that the Prophet (blessings and peace of Allah be upon him) drank from a 
    waterskin and a bucket, which usually needs both hands. Hence the scholars 
    granted a concession allowing the use of both hands when necessary.

    An-Nawawi (may Allah have 
    mercy on him) said: Our companions said: if he drinks with both hands cupped 
    and has a ring of silver on his finger, there is nothing wrong with that.

    End quote from al-Majmoo‘, 
    1/316

    Al-Qurtubi (may Allah have 
    mercy on him) said in his commentary on the verse (interpretation of the 
    meaning): “except him who takes (thereof) in the hollow [ghurfatan] of 
    his hand” [al-Baqarah 2:249]: Some of the commentators said: 
    al-gharfah means in the hollow of one hand and al-ghurfah means 
    in the hollow of both hands. And some commentators said that both mean the 
    same thing.

    ‘Ali (may Allah be pleased 
    with him) said: Hands are the cleanest of vessels. 

    The one who wants to consume 
    only that which is halaal nowadays with no doubts whatsoever should drink 
    with his hands water from springs and rivers at any time of night or day.

    End quote from Tafseer 
    al-Qurtubi, 3/253, 254

    If you carry the cup in both 
    hands, you should mostly use the right hand with the support of the left, 
    not the other way round, so that the left hand will not be the main one with 
    the right hand following or supporting it.

    And Allah knows best.