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One way with bash, files in between 20:00 and 22:00

#!/usr/bin/env bash

for f in /folder/x/*.bak; do
  var=$(date -r "$f" '+%H:%M')
  if [[ $var > '20:00' && $var < '22:00' ]]; then                                                                                                                                          
    echo "$f"
  fi
done

The above code should match your files.

That date syntax works on both GNU and BSD date(1)

EDIT: Updated answer

One way with bash, files in between 20:00 and 22:00

#!/usr/bin/env bash

for f in /folder/x/*.bak; do
  var=$(date -r "$f" '+%H:%M')
  if [[ $var > '20:00' && $var < '22:00' ]]; then                                                                                                                                          
    echo "$f"
  fi
done

• The above code should match your files.
• Just change to [[ $var < '20:15' ]] If that's just what you're after.
• That date syntax works on both GNU and BSD date(1)

EDIT: Updated answer

One way with bash, files in between 20:00 and 22:00

#!/usr/bin/env bash

for f in dir/*.bak; do
  var=$(date -r "$f" '+%H:%M')
  if [[ $var > '20:00' && $var < '22:00' ]]; then                                                                                                                                          
    echo "$f"
  fi
done

The above code should match your files.

That date syntax works on both GNU and BSD date(1)

EDIT: Updated answer

One way with bash, files in between 20:00 and 22:00

#!/usr/bin/env bash

for f in /folder/x/*.bak; do
  var=$(date -r "$f" '+%H:%M')
  if [[ $var > '20:00' && $var < '22:00' ]]; then                                                                                                                                          
    echo "$f"
  fi
done

The above code should match your files.

That date syntax works on both GNU and BSD date(1)

EDIT: Updated answer

One way with bash, files in between 20:00 and 22:00

#!/usr/bin/env bash

for f in dir/*.bak; do
  var=$(date -r "$f" '+%I:%M')
  if [[ $var > '20:00' && $var < '22:00' ]]; then                                                                                                                                          
    echo "$f"
  fi
done

The above code should match your files.

That date syntax works on both GNU and BSD date(1)

EDIT: Updated answer

One way with bash, files in between 20:00 and 22:00

#!/usr/bin/env bash

for f in dir/*.bak; do
  var=$(date -r "$f" '+%H:%M')
  if [[ $var > '20:00' && $var < '22:00' ]]; then                                                                                                                                          
    echo "$f"
  fi
done

The above code should match your files.

That date syntax works on both GNU and BSD date(1)

EDIT: Updated answer