During the 10 days of annual Desika utsavam for Purattasi Shravanam, adiyen will serve prasadam for the participating devotees between 1.30 PM to 3.30 PM. And during this period, there will be morning and evening aradhanams at the temple. Adiyen is confused as adiyen will be missing the afternoon Kalakshepam, Stotra Patham and Divya Prabandham classes. What must adiyen do?

Kalakshepams, Stotra and Divya Prabandha classes take place at all times; but Purattasi Shravanotsavam is only on 10 days of a year. To take part in the service of serving prasadam to the devotes during these 10 days is an opportunity to do a special service; hence, it seems one can prioritise this service over other classes.
Notes
The kind of services mentioned in this query – that is, serving prasadam to the bhagavathas, or attending kalakshepams and stotram and Divya Prabandham classes are Anugya Kainkaryams (kainkaryams taken on due to one’s own volition). These are not ordained kainkaryams; as such there is no question of superior of inferior classifications of these kainkaryams.
As these are not mandated kainkaryams, but take on due to one’s desire, there is no offence when any of them are not performed. It can be said that during these 10 days it is auspicious to serve prasadam to the bhagavathas.