My opinion differs from Forfarian (reply #17)
Had Alexander died in another parish a few days earlier, the church cleric would not necessarily have known this. It was very convenient for Ann to say the child’s father had ‘just’ died. It explained his absence at the baptism, and avoided any question of marriage for the sake of the child’s legitimacy.
I think James' marriage certificate is telling.
13 April 1861 at Southmuir, Kirriemuir (witness names have been cut off- who are they?).
James appears to know his father’s name, his father’s occupation (a ploughman in 1861), and that his father was not deceased.
In your previous thread, I brought to your attention the following Alexander Mitchell. He may be worth tracing through the records.
1861 census:- Alexander Mitchell, age 50, born Kirriemuir, is a ploughman at Whitehillocks Farm House in Cortachy and Clova. Head of house is David Mitchell 78.
(David was farmer at Whitehillocks in1841 and 1851 census too. Was Alexander a relative?)
1871 census:- the same Alexander Mitchell, age 63 (b abt 1808), born Kirriemuir is working as an agricultural labourer for James Findlay at Middlehill, Cortachy and Clova.