What is the expiation for not making up the Ramadan days I missed due to a legitimate Shar’i excuse at the age of fifteen? And must they be fasted consecutively or is it permissible to separate them? And how much is the expiation, with clarification on how to emancipate a slave in this era?

Delaying the make-up fasts of Ramadan (definition) until the next Ramadan is considered negligence and requires repentance. Its expiation after repentance is to make up the days along with feeding a poor person for each day that its make-up was delayed without a valid excuse (a mudd of the prevalent food of the country). The expiation is not repeated with repeated delays. The majority of scholars do not consider monetary value sufficient, but it is permissible according to the Hanafis and Ibn Taymiyyah out of need. Consecutive make-up is not required.