The incarnation of Narasimha happened in the evening on a Chaturdasi day. Mahapradosham is evening period of Trayodasi. Why then do we specifically worship Lakshmi Narasimhan during Mahapradosham period? Why do some say that during Mahaprodasham except SriNarasimha and SriRama, other Perumal-s such as Ranganathan must not be worshipped? What is the relation between SriRama and Mahapradosham period? Why do we offer Panagam for SriNarasimha?

The incarnation of Sri Narasimha was on Chaturdasi and not during Mahapradosham; generally, the evening period after sunset is called Pradosha kalam; based on which this period is special for Sri Narasimha. Moreover, the Agama-s have mentioned that aradhanam of Sri Narasimha during Mahapradosham period is special; hence we follow this.
The Agama-s say “nrisimhaM rAghavaM vinA” – one can also worship Raghavan during the Pradosha kalam; not sure about any other specific association that could exist. Because there is a mention in the Agama-s, some also worship Raghavan during the Pradosha kalam. Some others worship SriNarasimha only and not other Perumal-s.
Because it is said that Panagam is a special offering to Sri Narasimha and is included in our tradition, we do so.