Which books is best for this syllabus for semester exam in college ?

firstly you should go with college recommend book , and if you interested for more studying in nice way then refer naive set theory by Paul R. halmos..

other recommend books are mathematical logic ,2nd edition by Wolfgang Thomas and other is logic and structure by van dalen

any Indian writer are available for this?

for Indian writer , refer sm srivastava ( course on mathematical logic)..