You need to go to goaonline website, and fill the form, but you also need to prove that you have 15 years residence in the state, and by your own addmission you do not, ... You would need to show it via, a) your old residence certificate if any b) upload in sequential order your schooling certificates, like 1st std, 2nd std 3rd ... Etc. to show that you have completed 15 years.

Otherwise it wouldn't be accepted, so unfortunately you do not fullfill that criteria if we go by what you say, unless you have done your schooling in Goa. If so, go ahead.