The Kab Ha’yashar (chapter 96) discusses the widespread custom to position the Shamosh – the extra candle added to the Hanukah candles – specifically above the actual Hanukah candles, and he notes that this custom is alluded to in the verse (Yeshayahu 6:2), "Serafim Omedim Mi’ma’al Lo." The word "Serafim" here refers to a kind of angel, but it could also be read to mean "fires," such that the verse here describes fire situated above "Lo," which has the numerical value of 36, alluding to the 36 candles lit over the course of Hanukah. This verse thus alludes to the fires lit above the Hanukah candles, namely, the Shamosh. On this basis, the Kab Ha’yashar comments that the Shamosh is endowed with special sanctity which exceeds even that of the actual Hanukah candles, and therefore it may not be used for personal benefit, just as personal benefit is forbidden from the actual Hanukah candles. The Kab Ha’yashar decries the practice he observed of people making personal use of the Shamosh.
Hacham Ovadia Yosef, however, in Hazon Ovadia – Hanukah (p. 102, note 16), expresses astonishment over these comments of the Kab Ha’yashar (listen to audio recording for precise citation). He questions how the Kab Ha’yashar could reach such a ruling on the basis of a creative homiletic reading of a verse which is not actually discussing the Hanukah candles. Moreover, the entire purpose of the Shamosh, according to many sources, is to ensure that if one mistakenly derives personal benefit from the Hanukah candles, he would be considered as benefiting from the Shamosh, which is permissible for use, rather than the Hanukah candles. The very reason for lighting the Shamosh is the permissibility of using it for mundane purposes, and thus it is certainly not forbidden for use. Hacham Ovadia acknowledges that the Ben Ish Hai, in Parashat Vayesheb (14), cites an opinion forbidding personal use from the Shamosh, but he writes that the accepted Halacha does not follow this view. It is thus entirely permissible to derive personal benefit from the light of the Shamosh, as it is not endowed with any special status of Kedusha at all. (Hacham Ovadia also notes the view cited in Sha’areh Teshuba that if the room is fully illuminated, one may not benefit from the light of the Hanukah candles unless there are many Shamoshim near them, as the light of a single Shamosh does not contribute any light in a well-lit room. However, Hacham Ovadia rejects this opinion, too, and maintains that even if a single Shamosh is lit near the candles, one can be considered to be deriving benefit from the light of the Shamosh.)
Summary: It is entirely permissible to derive personal benefit from the light of the Shamosh.
