The transcription of the christening record lists no father and lists Jennet Wade as mother. There is a Jennet Wade who was christened on Jan 9, 1621 in Gainford (father George Wade) but she would have been 55 when Cuthbert was christened.90 Perhaps he was adopted by an elderly spinster?

From David Daniel Colpitts:
“I have found circumstansial evidence that proves Cuthbert Wade (Jr.) baptized on 25 Jun 1676, Gainford, Durham County, England is the son of Cuthbert Wade Sr. and his wife Jennet.  Cuthbert Wade Sr. was Parish Clerk of Gainford.  According to the Gainford Parish Baptismal record Cuthbert Wade Sr. (Gainsford Parish Clerk) had a daughter Mary baptized on 28th Nov. 1674.  The next record of Cuthbert Wade Sr. can be found in the Antiquities of Gainford, in the County of Durham which states, "1675- Cuthbert Wade, Clarke of ye Parish of Gainford buried ye 3rd day."  The next Wade baptism is that of Cuthbert Wade Jr, baptized 25 Jun 1676 son of Jennet, Widow, Gainford.  Thus, Cuthbert Wade Jr. was baptized after the death of his father, Cuthbert Wade Sr., Clerk of Gainsford Parish.”110