I live in Dutchess County, NY. I would like to know if I am obligated legally to pay for my husbands child support from his first marriage.

Absolutely not. HE is legally obligated to pay this out of his own funds. You are not legally obligated to pay a dime if you do not wish to.

He has the obligation to pay, they can of course garnish his paycheck, attach and freeze joint checking accounts and even put him in jail for failure to pay.

Is there a reason he is not wanting to pay ?