Who can claim for the funds of a deceased bank account holder?

There is not enough information in this question to answer it fully.  Were any people other than the deceased listed on the account?  If so, the account belongs to that person.  Did the deceased person leave a will?  If so, the contents of the bank account will be distributed according to the will.  If the deceased left no will and no joint account owner, then the law of your state will determine who receives the bank account.

In the situation you describe, it is likely that the children will receive equal shares of the bank account.