I have Term deposit on my relatives name, that is the money is mine but it is under my relatives signature authority. How I declare in the FBAR or should I not declare? I could not put it in my name as I was not present to sign the forms.

Technically, if the account does NOT have your name on it anywhere in th account, you do NOT have to submit the FBAR.

However, the spirit of the FBAR requirement is to identify foreign financial assets to make sure any income they generate is taxed according to U.S. tax law.

YOU have to decide if you are going to address the requirement from a technical aspect of the law or report as intended by the spirit of the law.

So if I have to declare as per the spirit of the law, under which part of the FBAR should I declare this?
Thanks for the help.

Under the JOINT portion (Part III), declaring yourself as the PRIMARY owner.

Its not just the 'spirit of the law' that requires reporting of a foreign account even if your name is not explicitly on the account.

. It is a technical requirement that an account someone has 'financial interest in or signatory or other authority' over be reported. If the money is yours (as you say), then you have a financial interest in it, irrespective of whether you have signature authority over it.

That is an accurate assessment which would push the OP to submit the FBAR.

However, if the IRS decided to do a cross-check on the account (where they contact the bank about the account in question), the bank would tell them that the OP did NOT have any signatory authority nor any financial interest at all, since his name is NOT on the account.

To my knowledge, there is NO penalty for claiming an account that show NO paper trail of ownership, but for sure the IRS would come back to the OP and ask WHY he put the account on his FBAR if his name is nowhere to be found as an owner. Once the OP explained the situation, the IRS would be satisfied, if slightly confused as to WHY the OP reported the account when "technically" he did not have to.

Also of course you do realise the family member does not have to give you the money back, I hope you trust them, We read here daily family members who don't return money