The "on it" is not necessary here.
When you stated "...with a small white patch..." this was already in reference to the bird, as a descriptive pretense, so where else would the patch be, other than on the bird? Does that make sense? It would be redundant.
The sentence also needs commas, so that a reader knows which word groupings go together. So perhaps:
A black bird, with a small white patch, eats to its fill , the fishes in the pond.
OR
A black bird...... eats to its fill of the fishes in the pond.
A comma OR a word like "of", "from", or "on" will work instead of the last comma.
I hope this helps.
Here is a link to a couple sites that might be of help to you:
- https://www.csun.edu/~sk36711/WWW/KAG/ch5.html
- https://app.grammarly.com/