Before 04 May 1637 John Gascoigne 1st Baronet (age 80) died. His son Thomas Gascoigne 2nd Baronet (age 41) succeeded 2nd Baronet Gascoigne of Barnbow and Parlington in Yorkshire.

In 1686 Thomas Gascoigne 2nd Baronet (age 90) died. His son Thomas Gascoigne 3rd Baronet (age 63) succeeded 3rd Baronet Gascoigne of Barnbow and Parlington in Yorkshire.

Before 04 Feb 1699 Thomas Gascoigne 3rd Baronet (age 76) died. His nephew Thomas Gascoigne 4th Baronet (age 40) succeeded 4th Baronet Gascoigne of Barnbow and Parlington in Yorkshire.

Around 1718 Thomas Gascoigne 4th Baronet (age 59) died. His brother John Gascoigne 5th Baronet (age 56) succeeded 5th Baronet Gascoigne of Barnbow and Parlington in Yorkshire.

In 1723 John Gascoigne 5th Baronet (age 61) died. His son Edward Gascoigne 6th Baronet succeeded 6th Baronet Gascoigne of Barnbow and Parlington in Yorkshire. Mary Hungate Lady Gascoigne by marriage Lady Gascoigne of Barnbow and Parlington in Yorkshire.

In 1750 Edward Gascoigne 6th Baronet (age 27) died. His son Edward Gascoigne 7th Baronet succeeded 7th Baronet Gascoigne of Barnbow and Parlington in Yorkshire.

On 10 Jan 1762 Edward Gascoigne 7th Baronet died. His brother Thomas Gascoigne 8th Baronet (age 16) succeeded 8th Baronet Gascoigne of Barnbow and Parlington in Yorkshire.

On 11 Feb 1810 Thomas Gascoigne 8th Baronet (age 64) died. His death believed to have been in part caused by the death of his only child Thomas Charles Gascoigne in a hunting accident four months earlier.Baronet Gascoigne of Barnbow and Parlington in Yorkshire extinct.