My mother passed away three years ago and my brother sold recently her condo ,split the money and put one amount of money (under 100000$) in one Serbian bank for me who live in USA Texas as an american citizen.
I am planing to transfer that money here to my personal bank account and my question is am I obligated to pay taxes after transferring that money here.
Sincerely

No - there are no taxes due from you for receiving this inheritance - so you owe no taxes to either the IRS or the state of TX. However, you shoud be aware that if the amount exceeds $100K you will have to file form 3520 with the iRS - see: http://www.irs.gov/pub/irs-pdf/f3520.pdf . Again, no payment is due, but you have to complete Part IV of the form.