Whether income earned on taxed retirement funds is chargeable to tax?

This question should really be asked of a accountant or lawyer well versed in tax law. But, from the information posted, and assuming there are no significant points omitted, in general: If the money deposited to your mother's benefit is in an traditional IRA, Spousal IRA, or other tax sheltered account, taxes are deferred on any returns in that account until they are withdrawn. At that time they are subject to ordinary income tax. The owner of the account, is responsible for those taxes. If the money is deposited in an account like an ordinary passbook savings account, interest bearing checking account, certificates of deposit, or other account that is not tax deferred, then the interest earned is reportable and taxed on the income tax return for the year in which the interest was earned. Again, the owner of the account is the person responsible for paying those taxes. There are certain accounts, such as a Roth IRA, in which the returns accumulate tax free, and are not taxed when withdrawn. There are numerous other types of accounts that have rules as to what is taxable and when that are specific to those accounts. The subject of what is taxable, when, and who is responsible for the taxes is far too complicated to be definitively answered in this type of forum.

I hope the question is Indian context. There are 2 things to be considered here. 1. When your father put in the money on your mother's name - did he 'gifted' that money to her. OR 2. Its just that he still considers that money as his own and has parked it in your mother's account. In case # 1 - its now your mother's money and if any tax has to be paid, where applicable. In case # 2 - your father will have to show your mother as a person whose income needs to be clubbed with his and then pay the taxes as per the limits applicable to him. Note that, in India tax rules (limits) are different for male and female.