Caroline
Your mans RN service was prior to the introduction of Continuous Service (1853) he is therefore unlikely to have a service record. Being under 18 also means that he is unlikely to have submitted a pension application to the Admiralty, but it could still be worth a check of the National Archives main catalogue in the ADM 29 series of documents. Your only other avenue, if you know the name of a ship he served on, is to look at her Ships Description book in the ADM 38 Series.
Martin