There is a custom observed by some Jews with roots in Aleppo to light an extra candle each night of Hanukah. This means that on the first night they light three candles one for the Misva, and two to serve as the "Shamosh" on the second night they light four, and so on. This practice is mentioned in the work "Derech Eretz," which documents the customs of the Aleppo the Jewish community (listen to audio recording for precise citation). The author writes that this custom was observed specifically by the "Kahal Kadosh Sepharadim" the community of Jews that observed the practices of the Jews of Spain. It appears that there was a particular segment of the Aleppo community that made a point of following the customs of the old Jewish community of Spain, and it was this segment which had the custom of lighting the extra candle.
The author of "Derech Eretz" mentions two possible reasons for this custom, in the name of Rabbi Yishak Tawil. One possibility is that the members of the "Kahal Kadosh Sepharadim" were wealthy and would always have two candles lit in their homes at night for illumination. (We have to remember that we are speaking of a time many centuries ago, before electricity, when not everyone had the means to properly illuminate their homes.) Therefore, the two candles lit the first night for Hanukah would not be recognizable as Hanukah candles, and so they decided to add a third candle to make it clear that the candles were lit for the Misva of Hanukah candles. And once they lit an extra candle the first night, they added an extra candle each subsequent night, as well. Another reason mentioned by Rabbi Tawil is that the members of this community were concerned about "Zugot" dong things in pairs a concept which the Gemara discusses in Masechet Pesahim, and which is based on the concern that this could pose danger. (Apparently, they were not concerned about having four, six or eight candles, but only two candles.) The custom therefore developed to add an extra candle the first night, and once this was done they added a candle each subsequent night.
Those whose forebears did not follow this custom should follow the more standard practice of lighting just one candle and a "Shamosh" the first night, and then one additional candle each subsequent night. It must be emphasized that those who do follow the custom must ensure to place the additional candle separate from the candle lit for the Misva. The custom is to add an extra "Shamosh," not to add an extra candle for the actual Misva, and therefore the extra candle, like the "Shamosh," must be positioned either away from or higher than the candle or candles lit for the Misva.
