As @Justin_Barrett mentioned, Airtable doesn’t provide control over individual attachments in the way that you would like.
As far as I know, there are no third-party tools that would be able to help you with this, either.
The only way that you could do what you want to do would be to separate out your attachments — each attachment as its own individual record — in a “join table” (aka “junction table”) that serves as the intersection between Table A and Table B.
So, you would create a new Table C, where each Attachment is its own record. Table A would link to some of those attachments in Table C, and Table B would link to some of those attachments in Table C.
(And once you have all of your attachments as their own records, that really opens you up to tons of other possibilities in the future, such as using Stacker as a front-end to control which users can see which attachments.)
Now, if you already have multiple attachments per Attachments field, you’ll need to separate them out individually to become your individual records in Table C. You would need to use Integromat to do this, by iterating through your attachments in each field and then creating your records.
Your Integromat scenario would be a simple 3-step scenario (see overview screenshot below), which would iterate through your “attachment field array” for each record that has attachments, and then it would create a new record for each found attachment:
Interestingly enough, @Moe has created an extension at miniextensions.com that does the REVERSE of what you want. His extension merges multiple Airtable attachment fields into one field. I’m tagging him here to alert him that there may be some demand for separating attachments as well.
In the meantime, Integromat would be your solution for separating your attachments.
p.s. If this is feeling a little overwhelming to you, and you have a budget for this project, and you’d like to hire an expert Airtable consultant to help you develop your system further, please feel free to send me a private message.