Regimental numbers were introduced in the late 1820s to ensure the regiment had the men the CO said they had. When issued he was the 106th most senior man in the regiment.
Only about 3-4% of Privates were allowed to be officially married. Once on the married establishment the army looked after the family, and took them on overseas postings.The army did not record details of families 'on the strength' until the late 1860s. If you have checked the regimental BMDs on Findpast (among other publishers) you only have the towns/forts recorded on the monthly musters so you can check nearby churches.
Once you have done the above you have a normal family history project. So try the IGI, family search.org etc; and as Jim says, the census, for overseas births.
Once you have his wife's maiden name, and if she was a widow, you can go back to the musters and look for a previous husband, also in the 39th Regiment. It was not uncommon for children to adopt the surname of a second husband. So bear that in mind.
Ken
