given the configuration of a plane.How can we decide maximum vertical height reached by it and how can we increase it??

Max. height is a combination of many factors, with (for a given aircraft configuration) the Density of air at that max. altitude being the critical factor

With more thrust (faster engine) you would get more lift thus more height before gravity & lift are equal again

Could try a different aerofoil section eg an undercambered wing for more lift

This has been discussed here at reply #45

indushekhar - you have asked the question in such a way that makes it
difficult - if not impossible to answer.

its like asking - given two legs what is the fastest a man can run and how can we increase it ?

tell us what particular plane you have in mind and then we can advise you.

otherwise all general questions will be met by general answers.