George A. Carthew, in his 'Hundred of Launditch and Deanery of Brisley' (1877) has a Barsham pedigree on p. 79, with some more detail than the Norfolk Visitation volume Darrell linked to above:
https://www.google.com/books/edition/The_Hundred_of_Launditch_and_Deanery_of/s05BAQAAMAAJ?hl=en&gbpv=1&dq=william+barsham+of+colkirk&pg=PA77&printsec=frontcover
According to Carthew, the William Barsham of Colkirk who married Anne Yelverton was the son of Thomas Barsham of Colkirk and Audrey Jennison (who married 2ndly, another Thomas Barsham, of Oxwick, first cousin to her first husband), and was grandson of Nicholas Barsham of Colwick.
Carthew abstracts the IPM of Nicholas Barsham of Colwick, who made his will 14 August 37 Henry VIII, and died the same day. The IPM was taken 26 Oct. 1549, when son and heir Thomas Barsham was age 17 years and more, so born by 1532. Per the Colkirk and Oxwick Parish Register, Nicholas Barsham was buried 15 August 1544.
Also per the parish register, Thomas Barsham and Audrey Barsham were married 25 June 1569. This was Audrey's second marriage to Thomas Barsham of Oxwick, meaning her first husband Thomas Barsham of Colwick (b. by 1532) was dead by 1569. Christopher Barsham, the third & youngest son of Audrey (Jennison) Barsham and her first husband Thomas Barsham of Colwick was baptized 9 February 1567/8. Audrey (Jennison) (Barsham) Barsham was buried 18 January 1571/2.
Per the same parish register, William Barsham, son of Thomas Barsham, was baptized 27 January 1557/8. This has to have been the William Barsham who married Anne Yelverton.
The will of William Barsham of Colkirk, dated 22 November 1630, proved 16 April 1636 [England & Wales, Prerogative Court of Canterbury Wills, 1384-1858], mentions Urith, daughter of Sir Augustine Palgrave, whom he intends to take to wife. This was Ursula Palgrave, baptized 3 March 1607/8 Barningham Norwood, Norfolk, married there 17 February 1630/1, William Barsham. She survived him, married 2ndly, Samuel Smith of Colkirk, and died 11 November 1680, buried at All Saints Church, Colkirk. See the pedigree on p. 18 of 'Palgrave Family Memorials' (1878):
https://www.google.com/books/edition/Palgrave_Family_Memorials/9NgKAAAAYAAJ?hl=en&gbpv=1&dq=william+barsham+of+colkirk&pg=PA11-IA22&printsec=frontcover
The William Barsham of Colwick (d. by 1636) who married as her first husband, Urith Palgrave above, was most likely the son of William Barsham and Anne Yelverton. I cannot locate any baptism, marriage or burial entries for Anne (Yelverton) Barsham, nor for any of the children she and William Barsham had, per the Barsham pedigree in the Visitation of Norfolk.
Administration of the estate of William Barsham of Colkirk was granted 1601. Perhaps this was the William Barsham (b. 1558) who married Anne Yelverton.
https://nrocatalogue.norfolk.gov.uk/index.php/barsham-william-of-colkirk-norfolk
Hopefully these dates will be of some help in further establishing the Barsham/Yelverton marriage.
Cheers, ----Brad