Some people offer a Nafilah (supererogatory) Salah (prayer) after the Adhan of Fajr is announced once they enter the mosque. Moreover, on commencing their Salah they promulgate their intention loudly saying, "I intend to offer such-and-such Salah.''
Is such a practice of theirs permissible?
No Nafilah except the stressed Sunnah of Fajr should be performed after the Adhan of Fajr is announced. Moreover, the stressed Sunnah of Fajr may replace Tahiyyat-ul-Masjid (two-unit Prayer to salute the mosque). Furthermore, the intention marking commencing a certain Salah is located in one's heart - i.e. promulgating it whether loudly or in a low voice, such as saying, "I intend to offer such-and-such Salah'' - is a Bid`ah (innovation in religion). However, if someone offers the stressed Sunnah of Fajr at home and then comes to the Masjid (mosque) before the Iqamah (call to start the Prayer) is announced, they may offer Tahiyyat-ul-Masjid.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.