My details
BA LLB (five year) with 3.7 GPA
GMAT first attempt : 610 second attempt: 500
Toefl: 110
Work experience : 1 year

Q:1) Is there any chances for me to a admission in
SUNY Binghamton, SUNY Albany or SUNY - Buffalo

Q2) Any idea which GMAT score they would use ( 610 or 500)

Thank you

Most schools will look at the higher of the two scores, even if it is an earlier score.

In general I think you'd be a hard sell at either of these schools due to your work experience. You'd probably want at least two years of experience to be competitive; with only one year they'll be looking for something else about your profile (great career advancement during your one year of work, or higher than average GMAT, for example) to show that you're ready for an MBA now.

Your alternative at this point would be pre-experience master's programs. Your GMAT might not be high enough to be competitive at top programs like the Kellogg MSMS or the Fuqua MMS, but perhaps there are less competitive options at other schools.