Legal Question in Real Estate Law in California

Your post is confusing. How can your father raise the amount you pay monthly on the mortgage (which is a misnomer, because the instrument is actually a deed of trust), unless he is the lender? But you use the word bank, which does not make sense. Are you asking whether your father can increase your rent?

Is it legal for him to raise it...

Yes, with some limitations.

If you have in force a written lease, those terms define how and when monthly payment can be increased. Seems you don't.

If you are month to month tenants, with or without written agreement, he has to give you at least 30 day prior notice of rent increase, then if you don't agree and pay, he can start eviction proceedings.

I suggest you negotiate settlement and get a written lease agreement. Otherwise immediately look for alternative lodging.