There is a Pudsey pedigree in Ducatus Leodiensis (acr 258) but not sure if/how they are related
Also, visitations of Yorkshire (acr281) has a Stephen Pudsey with a daughter Anne who might be the same person. However, the same pedigree is given in more detail in https://www.skiptoncastle.co.uk/craven-history/12_Parish-of-Long-Preston.pdf where it shows Anne Pudsey marrying John Wiseman. This same pedigree is also in Foster's Yorkshire, vol 2, acr 86
[S0337] John Burke, Esq and John Bernard Burke, Esq, Extinct and Dormant Baronetcies of England, Scotland & Ireland, The (2nd Edition), (London, 1841), 1841, Banks of Revesby Abbey; Page 34.