The origins of these devices is set out in Richard III as Duke of Gloucester and King of England by Caroline A. Halsted, volume 1, pages 404-5. The source quoted is Archoelogia vol. xxii, p.226. The main change here is to convert the text into modern English:
The dukedom of York – the falcon and fetterlock.
Conisbrough (presumably relating to ownership of the castle.) – The falcon, with a maiden’s head with her hair hanging about her shoulders and a crown on her head.
The Castle of Clifford – note, a property inherited from the Mortimers – a white rose.
The earldom of March – a white lion.
The earldom of Ulster – a black dragon.
(From Edward III) – a blue boar with his tusks and “cleis” and members of gold.
(From Richard II) – a white hart and the sun shining.
The honour of Clare – a black bull, his horns and his “cleys” and his members of gold.
(From the “Fair Maid of Kent” – a white hind.
(The principal connection with Joan Holland “the Fair Maid of Kent” is that Alianore Holland, Countess of March, her granddaughter, was the maternal grandmother of the 3rd Duke of York. Another granddaughter, Joan or Joanne, Alianore’s younger sister, married Edmund of Langley as his second wife.)