How you deal with those typical back biter(fellow worker ) ,they look/wait for minor mistakes of yours ,?

Whether in or outside the workplace, there will always be back-biters and gossipers. Always maintain professionalism and never stoop to their levels. You can prove their allegations wrong by performing well and doing contrary to what the gossips talks about you. If it is something that is libelous, you can confront the person but in a very proper way like inviting the person off from public.