There were around 345,000 British troops at Gallipoli in the Summer of 1915 so we're going to need a bit more detail about Wallis if we are to have any chance of identifying his unit. After a stalemate set in during the Autumn, a lot of troops were pulled out of Gallipoli and sent to Macedonia and Salonika. By mid January 1916 virtually all British troops had been withdrawn from the area. Most of the troops were taken to Egypt to reconstitute and re-equip. Unless Wallis was moved back to Britain among the injured, I doubt if he was available to father any children in Jan/Feb, although much will depend on his unit at the time.
How do you know he was at Gallipoli? Does someone have his medals?