Green’s Dictionary of Slang

1. the hand.

1823

Lamb Distant Correspondents n.p.: Those little short... puds [F&H].

2. a foot.

1984

Partridge DSUE (8th edn) 930/1: C.18–20.

3. a term of affection for a child.

1753		Richardson Sir Charles Grandison (1812) VII 617: He arose, took the little thing from me, kissed its forehead, its cheek, its lips, its little pudsey hands, first one, then the other.
1788		G.A. Stevens Adventures of a Speculist II 175: Speaking such love-formed words in the most innocent and affectionate manner – As for instance: ‘Budsy,’ and ‘Pudsy’.