The regular microfilm for Tynemouth for the 1820's is very hard to read (they should re-film it) so I go to an index that I have first then try to find it in the Bishop's Transcripts.
John Rochester Richardson is on page 300 of 689 or I don't know if this will work. It might direct you to a sign in page if you don't have an account then register it will be worth it:
https://www.familysearch.org/ark:/61903/3:1:S3HY-X43Y-WK?i=299&wc=9K5Q-829%3A13617901%2C30809801%2C31038502&cc=1309819The the LDS went through parish records they only put down names and dates. Since there are 2 Robert/Jane Richardson's in the area it is best to look at each one. I would also look through the burials.
There is a burial of a Thomas Richardson, age 10 days s/o Robert and Jane who was buried the same day as Matthew was baptised-4 Aug 1829. This happened alot. The minister may have said--is that one baptised? Nope---then lets do it now which would probably include any of their children not baptised and present at the time.
Another one is Robert Richardson buried 25 Oct 1827, age 10 mo s/o Robert and Jane of North Shields.
Matthew may have been older than someone being born 1829 or was a twin with the dead child Thomas
In some parishes the minister/priest wrote more into each entry than what was required. This one did and we are lucky for that. The burial entries gave parents names if they were children and spouse names also. Sometimes cause of death was written but usually the address was given. Baptisms have the address and the father's occupation.
Janis