I have relationship with Manufacturer for Paper products such as Toilet Tissue Rolls and other such papers which are consumable. I need an example of letter of supply for this commodity

You can't do that with government agencies. They put supplies out to bid. You can contact them and ask how to bid and when the next bid is. It might not be for years.
The only VA and DOD I know are the Veterans Administration and Dept of Defense. Is that who you mean, in the US?