From your question, it is not clear if you want to apply for a Visa or a Residence Permit. As such, I’ll give you both options, so you analyze them both and go from there. 1- In case you do indeed want to get a short-term student visa within Portugal, it is therefore possible to apply for a temporary stay visa for study purposes. Still, this application must be made outside Portugal, in the country of origin, or where you are legally resident. As such, it is not possible to do while staying in Portugal. 2- In case you want a Residence Permit for Students: It is not clear from your question if you are a High School or a University Student, nonetheless I will give you an answer for both. A) You are a High School Student that wishes to get a Residence Permit within Portugal: A Residence Permit can be issued for high school students, without having to leave Portugal, as long as they have entered legally, which is your case, given that you legally entered with your 24-day Schengen tourist visa that you got from Italy. B) You are a University Student that wishes to get a Residence Permit within Portugal: A Residence Permit can be issued for University students, without having to leave Portugal, as long as they have entered legally, which is your case, given that you legally entered with your 24-day Schengen tourist visa that you got from Italy. However, keep in mind that although it is one of the necessary requirements, the letter of acceptance from the educational establishment alone does not fulfil all the necessary requirements for issuing the visa. Other documents are also required, either for the issue of a new visa, thus having to leave the country, or for the issue of a Residence Permit, without leaving the country. Hopefully your doubts have been clarified.
