Wikipedia:
"Elizabeth "Libba" Cotten (1893–1987) was an American folk and blues musician. She was a self-taught left-handed guitarist who played a guitar strung for a right-handed player, but played it upside down. This position meant that she would play the bass lines with her fingers and the melody with her thumb. Her signature alternating bass style has become known as Cotten-Picking or Cotten-Style".

https://www.youtube.com/watch?v=R2DCWfBkMSI&list=RDeEoW1uLQvQA&index=8

Much has been written and said about Paul McCartney's weird fingerstyle technique, and if anybody asked me to give it a name, I might probably call it "McCartney's thumb and index-fingerstyle" or "McCartney's picking and strumming pattern". If you are used to play "proper" fingerstyle, it's not advisable to have a go at this weirdo, cause you might end up with the same problem that I had, when I tried to nail down Lindsey Buckingham's odd picking pattern he uses on Fleetwood Mac's "Never Going Back Again". It took me approximately 2 days to get it into my head with the result, that I had problems afterwards to play the other stuff again, such as "Scarborough Fair", for instance. Guess I had to rearrange my synapses first, that somehow got into disorder ...
Nevertheless, "Blackbird" is a classic fingerstyle songs that simply can't be overlooked. So let's have a go at it. McCartney plucks two strings with his thumb and index-finger simultaneously. Then he strums the treble strings with his index-finger again and that's it. The D-String leads a rather lonely life and is only plucked three or four times during the song. Now forget about all this and let's try to activate the remaining two fingers of the picking hand, as well.

BLACKBIRD (The Beatles)

Written by Paul McCartney in the key of G in 2/4 time
Released on the album: The Beatles / The White Album (1968)
Blackbird on Wikipedia

thumb: x             Hammer on: h             Bend up: V                   Play or don't: ()
index: a             Pull off: p              Bend down: Λ                 Break: b
dirty: b             Slide up: /              Fret but don't pick: !       Downward stroke: ↑
ring: c              Slide down: \            Staccato: :                  Upward stroke: ↓
pinky: d             Arpeggio: ~~~            Mute: m

To stabilize your picking hand, put your ring on the e-string in the red marked part
Red colored exclamation marks offer additional fretting information
Stay with your pinky on the b-string in the green marked part

INTRO

e----------------------------------------|  picking pattern: 
b---0----------1a----------3d--------/---|  xb - a (3x)
g--------0-----------0-----------0-------|
D----------------------------------------|
A--------------0-----------2a--------/---|
E---3c-----------------------------------|
    <----------- 6/8 ------------>

e----------------------------------|-----------------------------------|  picking pattern:
b---12d-------12d-------12d--------|---12d--------12d-------12d--------|  xb - a - b - x - b - a (2x)
g---------0-------------------0----|----------0--------------------0---|
D----------------------------------|-----------------------------------|
A---10a------------10a-------------|---10a-------------10a-------------|
E----------------------------------|-----------------------------------|
          <---- 4/16 ----->                   <---- 4/16 ----->

e----------------------------------|------------|  picking pattern:
b---12d-------12d-------12d--------|---12d------|  xb - a - b - x - b - a
g---------0-------------------0----|------------|  xb
D----------------------------------|------------|
A---10a------------10a-------------|---10a------|
E----------------------------------|------------|
          <---- 4/16 ----->            1/2