Show custom post type in archive page by category

There is no concept natively of archive for intersection of specific custom post type with specific taxonomy.

There are multiple approaches here, but all will take some tinkering:

  • you can adjust category term archives to include your CPT (via pre_get_posts hook)
  • you can extend custom post type archives with endpoint to filter them by category
  • probably more ways, it gets pretty arbitrary outside of native functionality

In your specific case I find it a little strange that CPT in question is a “Blog”, since that’s what native posts already are (and likely easier to go with for, well, blog).