You can't change your caste by paying late fee. 

Before the jee exam only you need to change the caste from any government office. 

You can change your caste by taking a study certificate from your school and then apply to change Caste . Then the government officer will tell about the duration for the change of caste. 

I think you need not to be panic now.Its not too late to change you can change it nowitself because it may be useful for your future use. 

If you are lucky changing of caste may happen faster.  

Hope your need to be fulfilled. 

Thank you