There is an interesting custom that the Ben Ish Chai in Parashat VaYeshev (Hlacha 28) brings down for Rosh Chodesh Tevet. He said there is a custom in the Shul to light a special candle on Rosh Chodesh Tevet for the respect and remembrance of Rabbi Meir Ba’al HaNes. It’s brought down by the great Mikubal Rav Saliman Musafi, that when ever you give charity in memory of one of the Tzadikim, or when you light a candle in memory of one of the Tzadikim, you say ‘Hareni Noten Tzadaka’ or ‘Hareni Madlik Ner Ze’ continuing with ‘Lichvod Adonenu VeRabenu HaTzadik [name] Ben [name]’ instead of "Lielu Nishmat". So he is saying that you shouldn’t say, Lielu Nishmat (for the soul of.) So on Rosh Chodesh Tevet, one should say that they are lighting the candle in honor of our esteemed Rabbi Meir Ba’al Hanes. It is always a big Zechut (commemoration) to light candles in their honor for they represent and stand for us in Shamayim (heaven.)
Therefore the custom again, on Rosh Chodesh Tevet is to light an extra candle. You should light on the night or day of Rosh Chodesh itself, which means you light on the night or day of the first of Tevet. (You do not light on the night of the 30th of Kislev, when Rosh Chodesh is two days.) You light it away from the Menorah, aside from the Menorah. You light an extra candle, out of respect for the Tzadik Rabbi Meir Ba’al Hanes.
Furthermore one does not have to light this memorial candle at the same time that he is lighting the Menorah. It may be done before or after.
For a detail biography on Rabbi Meir Ba’al HaNes, copy and paste the link below into your browser:
http://judaicaplus.com/Tzadikim/tz_viewer.cfm?id=211&page=meir.htm&t=Rabbi%20Meir%20Ba%27al%20HaNess