My mom asked what's my ssn for house mortgage ?

She only needs ot do that if you will be responisble for the mortgage, which you do't' want to be.  So no.

She can't just "add you" to the mortgage. She's trying to make you a co-owner.  And the BANK is the one who would ask for your SSN.  Don't give her your number--and find out what the heck is going on.  Don't SIGN anything. 

If you aren't 18, she can't legally have you on the paperwork. 

If you're over 18, don't give it to her. Your name on the contract means you're liable for making payments if she doesn't.  It can ruin your credit rating horribly.  

Take it as a red flag, do NOT get pulled into this.

Did you agree to be legally responsible to pay her mortgage? If not, there’s no reason they would ever need your info. Something shady is going on. 

She doesn't need to add you to her mortgage unless she's also tying you in to being responsible for paying it back. 

She doesn't need to add you to her mortgage. She can't do it without your signature either. If you go on the mortgage as a co-borrower, you are equally liable for the payments. My guess is that her income and/or credit isn't good enough to get a mortgage on her own.  Hopefully you haven't given her the information. 

If you already have a home and mortgage you mother's lender will take that into consideration.  Conversely if you don't own a home yet it could effect your chances of getting a mortgage.

Its up to you, but I wouldnt do it. If she defaults on her mortgage, and her assets are insufficient to cover the debt, then YOU have to make up the remainder. I mean, you know her, and you know how likely she is to cover her mortgage, but I wouldnt do that for a family member. 

If your added to the mortgage then you will owe the money if she doesn't pay it. She's making you a co-signer.