Steps to add the custom choice column as filter in custom query webpart:
1. export the webpart after selecting library on which you want to apply the filter.
2. open exported webpart with SPD.
3. search for< CommonViewFields> property in it and add the column name there on which you want to filter.
4. now search for <property name="AdditionalFilterFields" type="string" /> and edit it as <property name="AdditionalFilterFields" type="string" >Your Column name here </property>
5. save the webpart and import it in the page and apply, the column will now available in the filter.
******Steps to find the column name
1. site action > view all site content > select your library
2. Select setting>list setting all the columns of list are available to you in columns area.
3. hover mouse over the field, in status bar you can view some thing as below
the fieldname bold above is your required column name.
If works please marked as answer