if wife live with other person what legal action should be taken.

you can approach the family court in your area and ask for divorce on teh grounds that she is living with another man after making allegations of dowry harassment against you. 

If you have conclusive evidence (which your lawyer can advise) her maintenance petition will be dismissed. 

Your lawyer is best and only person to advise as s/he is well aware about facts and circumstances of the case, an able, competent and intelligent to satisfy you and proceed, if you have faith in him/ her.

You can not take action against that man, but present such evidence of living together with the relationship of wife with another man and seek divorce without maintenance. Your advocate may suggest how to get such valid evidence.

Have you apprised the Court of the alleged adultery on the part of your wife in defence of the maintenance petition.?