anyone here knows EU Law?

Can I apply residence permit while holding (3 months) Schengen Visa (Tourist Visa)? It is a long story, briefly to say, I have studied few years at a EU country, now I'm at Canada and I couldn't go back since my old residence permit was expired and due to insufficient financial statement M.V.V. also got rejected. Consul suggested me to apply Tourist Visa at least I can go back for 3 months. But I'm worry about after 3 months I have to leave the country again, anyone has any ideas? Million thanks.