Qadha for not fasting

I am a student aged 20 yrs old. I have missed a lot of fasts almost all during past months of ramadan except this one. With Allah's grace, I came very close to islam this year, praying regularly even the tahajjud prayer and fasting almost daily. I have read about the compensation of breaking fasts that is 60 foods for poors or 60 days fasting for 1 fast. As I am a student so I cant afford food for poor people so I fasted almost 4 months consecutively as a compensation for 2 fasts but then after some research I came to know that the compensation for fasting is only for those who "break" it by intercourse, eating e.t.c and not for those who "leave" them. For every fast a person left out of ignorance in past, he only have to fast 1 day for 1 fast. My question here is that, I have fasted 4 months with the intention (niyya) of compensation for 2 fasts but is it right that those fasts can be recorded as compensation for 4 months of fasting (1 fast for 1 day) so i have completed the compensation for 4 months of ramadan fasting that I have left in the past and not just the 2 days even if I don't have the intention of every fast to be for 1 fast i left before.