| Date | Competition | Home | | | | Away | Scored | MOTM | | | |
| 02/09/2020 | First Division | DARLINGTON RAILWAY ATHLETIC |
0
|
V
|
1
| RICHMOND TOWN | 0 |
|
|
|
|
| 05/09/2020 | First Division | RICHMOND TOWN |
1
|
V
|
1
| DARLINGTON TOWN | 0 |
|
|
|
|
| 12/09/2020 | First Division | RICHMOND TOWN |
6
|
V
|
0
| DURHAM CORINTHIANS | 0 |
MOTM
|
|
|
|
| 03/10/2020 | First Division | RICHMOND TOWN |
5
|
V
|
2
| WINDSCALE | 0 |
|
|
|
|
| 07/10/2020 | First Division | BOLDON C.A. |
4
|
V
|
1
| RICHMOND TOWN | 0 |
|
|
|
|
| 14/10/2020 | First Division | WASHINGTON UNITED FC |
2
|
V
|
2
| RICHMOND TOWN | 1 |
|
|
|
|
| 24/10/2020 | First Division | RICHMOND TOWN |
3
|
V
|
0
| ANNFIELD PLAIN | 0 |
|
|
|
|
| 28/10/2020 | First Division | SILKSWORTH COLLIERY WELFARE |
2
|
V
|
0
| RICHMOND TOWN | 0 |
|
|
|
|
| 05/12/2020 | First Division | WINDSCALE |
3
|
V
|
1
| RICHMOND TOWN | 0 |
|
|
|
|
| 12/12/2020 | North Riding Cup | Wiggington Grasshoppers |
2
|
V
|
0
| RICHMOND TOWN | 0 |
|
|
|
|
| 17/04/2021 | The Alan Hood Charity Cup - 1st Round | RICHMOND TOWN |
2
|
V
|
3
| DURHAM CORINTHIANS | 0 |
|
|
|
|
| 24/04/2021 | The Alan Hood Charity Cup - 1st Round | RICHMOND TOWN |
5
|
V
|
4
| HORDEN COMMUNITY WELFARE | 0 |
|
|
|
|
| 01/05/2021 | The Alan Hood Charity Cup - 1st Round | GATESHEAD LEAM RANGERS (WEAR) |
4
|
V
|
0
| RICHMOND TOWN | 0 |
|
|
|
|