Known children of Alexander Smith and Margaret Roger:
05 Apr 1768 - William Smith
12 May 1771 - John Smith
18 Apr 1773 - Alexander Smith
28 Nov 1777 - Alexander Smith
28 May 1775 - James Smith
19 Mar 1781 - Agnes Smith
03 May 1785 - Alexander Smith
19 Aug 1787 - Josiah Smith
There are birth records for three sons named Alexander to this Alexander Smith and Margaret Roger. FamilyTree records for the multiple Alexanders have over time been erroneously combined into a single record.
It's possible that the first two sons died at an early age and the subsequent son was named the same. One difficulty with this theory is that if the last Alexander was born in 1785, he would have been only 17 when married and when first child Jean was born. Any other details or explanation would be greatly valued.
If this is correct, then this Alexander, Jr. was barely 16 when married and only 17 when first child William was born. This casts some doubt on the veracity of this relationship.