The Grassy Gnoll
Explorer
Page 107, Players Handbook, under Pact of the Chain.
The PHB also stats out the relevant 'special' familiars (imp, quasit, pseudodragon, sprite) at the back of the book but there is no mention of their magic resistance being transferable to the warlock. The only reason they are listed on the PHB is in order for warlocks to check them out.
There are variants of each in the MM that permit them to be familiars where they do transfer their powers.
But in the spell description for Find Familiar it specifically states that a familiar summoned by the spell can take the form of a bat, cat, crab*, frog/toad, hawk, lizard*, octopus (!)*, owl, poisonous snake, fish*, rat, raven, sea horse*, spider* or weasel*but that the familiar is a spirit (fey, celestial, or fiend) in fact, and only assuming those forms (where marked with *, there are no stats on the PHB). It says you can cast a touch spell through them and gain the advantage of any special senses they have but nothing about resistances. That info exists only in the MM.
So on the face of it it appears that as written a warlock's 'special' familiar is not intended to share its resistances, although in the MM they do.
It is a strange one, as the casting of FF does not by RAW permit the summoning of one of these creatures, they are not summoned to be dismissed back to the Dimension Where Spare Socks Live, but rather are made pacts with on their own terms rather than being a Fey/Fiendish/Ineffable Flunkey of a greater power.
So my gut says nope.
The PHB also stats out the relevant 'special' familiars (imp, quasit, pseudodragon, sprite) at the back of the book but there is no mention of their magic resistance being transferable to the warlock. The only reason they are listed on the PHB is in order for warlocks to check them out.
There are variants of each in the MM that permit them to be familiars where they do transfer their powers.
But in the spell description for Find Familiar it specifically states that a familiar summoned by the spell can take the form of a bat, cat, crab*, frog/toad, hawk, lizard*, octopus (!)*, owl, poisonous snake, fish*, rat, raven, sea horse*, spider* or weasel*but that the familiar is a spirit (fey, celestial, or fiend) in fact, and only assuming those forms (where marked with *, there are no stats on the PHB). It says you can cast a touch spell through them and gain the advantage of any special senses they have but nothing about resistances. That info exists only in the MM.
So on the face of it it appears that as written a warlock's 'special' familiar is not intended to share its resistances, although in the MM they do.
It is a strange one, as the casting of FF does not by RAW permit the summoning of one of these creatures, they are not summoned to be dismissed back to the Dimension Where Spare Socks Live, but rather are made pacts with on their own terms rather than being a Fey/Fiendish/Ineffable Flunkey of a greater power.
So my gut says nope.