The biggest problem is that Sussex is a county densely populated with people who over the centuries have had their surnames transcribed as Tuppen, Tupper, Tuppin, and occasionally Turpin, any of which could come from your ancestral line. Loads of us at this end would love to assist so could you tell us the name and either birth or marriage details of the last ancestor you are certain of and if possible add the Sussex parish they came from.
For example, a William Tuppen, baptised 1680, son of William appears in Rottingdean (then a downland parish with sheep in abundance) but was he yours? With info like that, many of us will be able to start digging into the local records on your behalf.
Roy G