If you look in the Selborne registers, you will find:
1705 25 Sep., Mary Minivy, bastard child of John Minivy, carpenter of Broad-Windsor in Dorset, and Anne Skelton, baptised in Selborne
So I went to:
Broadwinsor registers
1696 2 Feb., John Menyfye of Abbots Stoke* married Joan Dennis of this parish.
1696 [no date], Elezabeth Minnyfre, child of John, baptised.
1701 19 Oct., John Minnifie, child of John, baptised.
1718 22 Jun., Henry Menneffie, son of John, buried.
* - probably Stoke Abbott?
Using Family Search - I came across lots of people with the name in Dorset - here are just a few@
Stoke Abbott registers
1578 29 June, Thomas Mynifie married his wife.
Sherborne, Dorset:
1789 30 Jan., Thomas Minifie, child of John and Elizabeth, baptised.
1792 15 Feb., John Minifie, child of John and Elizabeth, baptised.
1793 29 May, Ann Jane Minifie, child of John and Elizabeth, baptised.
1802 17 Mar., Eliza Minifie, child of John and Elizabeth, baptised.
1803 30 Mar., James, child of John and Elizabeth, baptised.
1805 7 June, Jane Minifie, child of John and Elizabeth, baptised.
1808 27 Feb., Charles, child of John and Elizabeth, baptised.
1810 22 June, John Minifi, child of John and Elizabeth, baptised.
Also, earlier
1728 1 Oct., Humphry Minivy, child of John, baptised.
1607 3 Dec., John Menfie, child of John, baptised in St Mary’s Beaminster.
1636 15 Nov., John Minifie married Amy Body “
1687 25 July, John Minyfee was buried. “
etc., etc. Yours Jane