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If I was to purchase this record would I see any information on his mother Ms Taylor?

Highly unlikely, unless she was involved in whatever he was convicted of.

What do you mean by 'trailed'?

Hi forfarian, I have no proof, only it came up on ancestry DNA, I have also seen names on somebody else’s tree! Obviously 🙄 these aren’t to be trusted, I normally go back through the census, birth, marriage and death certificates, but John has been very challenging, maybe because I’m barking up the wrong tree 🌳
So you think Archibald and Agnes are the way to go?

You are absolutely right not to trust anything you find online, and especially not other people's trees on commercial web sites like Ancestry.

In my opinion Archibald and Agnes are a better fit for the parents of John Baird because
(a) John's first son was named Archibald
(b) they were in Mauchline, which is where Archibald was baptised
(c) he is the right age to be the one in the census in Edinburgh in 1841
so I would definitely want to investigate them if I were you.

It may be that Archibald (senior) was related to William-husband-of-Mary-Gibson which could account for a DNA match.

It is also possible that your John Baird is one of the many people whose baptism record, if it ever existed, has not survived.

But don't trust me either! Make sure to leave no stones of your own unturned.

John Baird was the Son of William Baird and Mary Gibson b. 22 Aug 1784 (Scotland's People).

Yes.

Below is the christening date for Archibald, John and Helens 1st Son.
Name:  Archibald Baird.  Event Type:  Christening.  Event Date:  24 Jun 1818.
Event Place:  Mauchline, Ayrshire, Scotland.  Event Place (Original):  Mauchline, Ayr, Scotland.
Gender:  Male.  Birth Date:  5 Jun 1818.  Father's Name:  John Baird. Mother's Name:  Hellen Watson.

Yes.

But what is your evidence to prove that John Baird, husband of Helen Watson and father of Archibald is the same person as John Baird, son of William Baird and Mary Gibson?

If that census is the right family, John's age is recorded as 45, which means that he was born between 1791 and 1796. John Baird, born in 1784, if he was still living in 1841, would have been 56 and should have been recorded as 55 - a full ten years older.

The most obvious candidate to be father of John Baird, father-in-law of Helen Watson, and grandfather of Archibald is surely John, son of Archibald Baird and Agnes Bell, who was baptised in Mauchline on 3 January 1796?

I happened to be wandering around Tyrie yesterday and came across Denburn. See attached.

The name Denburn is on the glass panel above the front door.

This looks like the right ones in Madon Bank, St Cuthberts, Edinburgh in 1841.
John Baird  45, Gardener
Helen Baird  45
Jane Baird  20
John Baird  15
Wm Baird  15
Elbert Mcallister  40
Euphemia Mcallister  40

FreeCEN transcribes the address as Meadow Bank, and the McAllisters are Gilbert and Euphemia, in a separate household, so there's nothing there to help with the Baird family. SP and FindMyPast also say Gilbert not Elbert. I assume, therefore, that the foregoing is from Ancestry.