State does sponsor H-1B since i am one of 'em. If you already have a state job, then talk to the state office attorney. If the H-1B falls under the same quota or not, it depends on the nature of job. If they have a lab and all facilities where your expertize is being utilized, then its out of the quota; but if its a  desk job or even field work, then it does fall under quota system.

Hope it helps.