Hi @Benr,
Great question, and thanks for asking it!
This approach will only work in Specify 7 (not 6), so when managing your Accession data, you will need to use that platform.
In your “Field Formatters” (UIFormatters) app resource for the collection/discipline, you can configure a format like the one you’ve described here:
<format system="false" name="PostfixAccessionNumber" class="edu.ku.brc.specify.datamodel.Accession" fieldname="accessionNumber">
<field type="constant" size="4" value="ACC/"/>
<field type="numeric" size="5" inc="true"/>
<field type="regex" size="0" value="( [A-Za-z])?"/>
</format>
After this is set, you should see ACC/#####( [A-Za-z])? shown in the preview for the field. Now you can enter ACC/10001 A and it will be valid! It will also increment based on your postfix.
To make this look much nicer and be easier for the user, you can update the Accession view definition so that it uses the appropriate default (add default="ACC/#####" to the field):
<cell type="label" labelfor="1"/>
<cell type="field" id="1" name="accessionNumber" uitype="formattedtext" default="ACC/#####"/>
That’s better! 
Now you can create Accession records with an Accession Number that may or may not have a postfix. It also supports incrementing based on the postfix!
Video Demonstration: