The fact hat you cannot find a baptism for the child is not unusual. To find a baptism you would have to look through Parish records for every Church in the area. Not all records are online, so you would need to go to the local archives. Cheshire quarter sessions would cover a wide area. You have not given any details of the name you are looking for, so it would be difficult to help you find this. You can check the Court proceedings through from beginning to end, but this again would mean going to the Archives in the area and starting at the first hearing, then see if there was a date given for the next part of the proceedings.