This is the 4226th most frequent Japanese word.
付か
The term "付か" is not commonly used on its own in standard Japanese and might be a fragment of a conjugated verb, such as "付く" (tsuku), meaning "to attach" or "to stick."
The word '付き' here is derived from the verb '付く', used to indicate that a scratch (being an attachment or mark) can easily adhere to the material.
これは傷が付きやすい素材です。
This material is prone to getting scratches.
The word '付いて' is the conjugated form of '付く', signifying that the ink unintentionally adhered to the hand.
手にインクが付いてしまった。
The ink got on my hand.
The word '付いている' reflects a state where something abstract (persuasiveness) is attached to his proposal, indicating acquisition or presence.