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I've no idea what you may have already checked, so apologies if you know this already.
Have you already checked what entries there are on the FamilySearch site? The index covers this parish. The registers only begin in 1680, so relatively limited coverage of the 17th century.
There are baptisms for two sons, George in 1699 and John in 1697 where the father is named John. There is a marriage of a John Haines to a Frances Masters in Mottiston in 1695, probably the parents.
A John Haines died about 1725 and left a will, copy available at Hampshire Record Office, ref 1725AD/053. This is probably John senior since there is another one in 1747 for John Haines of Mottistone, maltster ref 1747AD/080.
Hope that helps
Nell