According to Burke's Heraldry, "[T]he heiress of Sir Robert Barnham, second and last baronet, married Thomas Rider, esquire. A branch of the Barnhams still exists at Norwich."
From: 'House of Lords Journal Volume 18: 28 November 1707', Journal of the House of Lords: volume 18: 1705-1709 (1802), pp. 346-48. URL: http://www.british-history.ac.uk/report.asp?compid=29576. Date accessed: 04 January 2007.
Puleston & al. versus Puleston & al.
Upon reading the Petition and Appeal of Dame Martha Puleston, Widow and Relict of Sir Roger Puleston Knight deceased, Priscilla Puleston, and Martha Puleston, Daughters of the said Sir Roger Puleston, both Infants, by the said Dame Martha Puleston their Mother and next Friend, from an Order and Decree made in the Court of Chancery, in a Cause there depending, between the Petitioners Plaintiffs, and Thomas Puleston Esquire and others Defendants, the Twenty-third Day of February One Thousand Six Hundred Ninety-eight; and also from another Order or Decree, made upon the Re-hearing of the said Cause, the Seven and Twentieth Day of July One Thousand Six Hundred Ninety-nine; and all other subsequent Orders and Proceedings grounded thereupon, in respect to several Annual Payments in the Decree mentioned; and praying, "That the same may be reversed and set aside; and that the said Thomas Puleston, an Infant, Son and Heir Apparent of the said Sir Roger Puleston, Philadelphia Ryder, Widow and Executrix of Thomas Ryder Esquire deceased (who was the surviving Executor and Devisee named in the last Will and Testament of the said Sir Roger Puleston) and Barnham Ryder Esquire, Son and Heir, and also the other Executor, of the said Thomas Ryder, may answer the said Appeal; and that Notice of this Order to their several Clerks in Court may be good Service, in order thereunto:"
It is Ordered, by the Lords Spiritual and Temporal in Parliament assembled, That the said Thomas Puleston, Philadelphia Ryder, and Barnham Ryder, may have a Copy of the said Appeal; and shall and they are hereby required to put in their Answer or respective Answers to the same, in Writing, on Friday the Twelfth Day of December next, at Eleven a Clock in the Forenoon; and that the Service of this Order upon their Clerks in Chancery shall be good Service, in order thereunto.
Transcribed from Le Neve's Pedigrees of the Knights: Sr Barnham Rider Kt made so at the coronation of King George.