I think that John MORGAN was legitimate, but that Peter MORGAN was probably his uncle, rather than his father. I think his parents were Matthew MORGAN and Susan/Susannah and that John was a posthumous child, born 4 months after his father's death.

There are 2 sets of baptism records that can now be searched and viewed online - the original parish church register (PR) and the Bishop's Transcripts (BTS). The BTS were a copy of all entries, taken at the time, for submitting to the local Bishop. They sometimes contain slightly different information, as they do in the case of John MORGAN.

All at Plemonstall/Plomstall
PR
John son of Susan MORGAN of Hool was bap. 15 Dec 1728.
BTS
John son of widdow MORGIN bap 15 Dec 1728.

Matthew MORGAN of Hool, Blacksmith, buried 4 Aug 1728.

Susannah MORGAN of Hoole buried 6 Feb 1739.

If John MORGAN had been illegitimate, then the minister of the time would have said this quite clearly in the register, e.g. "Thos. a bastard son of Thos. PROFIT bap. 6 Aug 1714." Illegitimate children would have become the responsibility of the parish if the father was not identified, so the authorities made every effort to make them pay. Bastardy Orders are listed in the Chester Quarter Sessions Poor Law Documents, but unfortunately those available online only go from 1730/31 - 1746.

There are baptisms of Matthew, 17 May 1703 and Peter 23 Dec 1705, both sons of Matthew MORGAN/MORGIN of Mickle Trafford. These could be John's father and uncle.

The records at Plemonstall of that time only list the father's name. There are a number of children born to Matthew (bearing in mind that they may be the children of 2 different Matthews, even father and son!).

Mathew 17 May 1703
Peter 23 Dec 1705
Mary 23 May 1708
Catherine 17 June 1714
Joseph 24 Aug 1718
Martha 14 Jan 1725

Children of Peter
Mary 14 Oct 1733
Peter 10 Oct 1736
Joseph 6 Nov 1738

Your John born 1728 may have been brought up with his uncle's Peter's family. Looking at the dates, and bearing in mind that Susannah died in 1739, the fact that Peter's last child was 1738 could suggest that Susannah, widow of Matthew, could have been the mother of the later children as well. Although against the law at that time, it may have been the pragmatic thing to do!