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

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.