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