The affix ṭhak comes in the sense of 'who studies there' after a word in the Locative -7th case in construction, denoting an improper place or time.,
The word अदेशकाल means the time or place of study, which is prohibited by sacred institutes. अध्यायिन् means one who studies. Thus श्मशानेऽधीते = श्माशानिकः 'who reads in a funeral ground.' चतुष्पथिकः 'who studies where four roads meet.' So also चतुर्दश्यामधीते = चातुर्दशिकः, 'who reads on the 14th lunar day.' So also आमावास्यिकः ॥
Why do we say 'improper time and place ?' Observe स्रुघ्नेऽधीते, पूर्वाह्णेऽधीते ॥,