Praise be to Allah, and may peace and blessings be upon the Messenger of Allah. To proceed:
First: There is no evidence that an itchy hand is a cause or sign of provision
Associating an itchy hand with the arrival of money or provision is a common belief among people, but it has no basis in Islamic teachings, nor is there any sound empirical evidence for it.
Itching may occur because of:
Nerve-related factors,
Allergies,
Or other known medical and natural causes.
As for believing that it is a definite sign that money or provision is coming, this is one of the superstitions commonly spread among people.
Second: Why is this belief prohibited?
Because a Muslim should only regard something as a cause when it is:
Established by Islamic revelation,
Or established through reliable experience and observable reality.
Ascribing a causal effect to something without religious or empirical evidence is incorrect.
For this reason, some scholars have stated that attaching one’s heart to imaginary causes may fall under minor shirk, because a person attributes an outcome to something that Allah has not made a cause for that outcome.
Third: Provision is in the hands of Allah alone
The believer knows that all provision comes from Allah alone.
Allah says:
“And in the heaven is your provision and whatever you are promised.”
Therefore, a Muslim should:
Place their trust in Allah,
Take the proper and legitimate means,
Make du‘a,
And strive to earn their provision.
As for imaginary signs, pessimistic omens, and attachment to superstitions, a Muslim should not base beliefs upon them.
Summary
An itchy hand does not indicate, either religiously or empirically, that provision is coming.
Associating it with money or good fortune is one of the superstitions commonly spread among people.
One should not believe that something is a cause of provision unless there is sound religious or empirical evidence for it.
All provision is in the hands of Allah, and it should be sought through legitimate means while placing one’s trust in Him.
And Allah knows best.