When I think of Rodgers I automatically think of Joseph Rodgers & Sons and the famous Star and Maltese Cross trademarks, but this blade makes no mention of the sons, neither does it have the trademarks, so if it is from the same lineage it is much earlier.
The firm has no universally recognised start date, but are known to have been working as cutlers since before 1724 - John Rodgers is recorded in the records.
The trademark was claimed earlier to but only conferred in 1764 to Joseph Rodgers - it wasn't used on all items at that time, mainly being seen on pen and pocket knives. Then there is the Royal Warrant - "Cutlers to His/Her/Their Majesties", granted around 1821 - this isn't on the blade either.
Another hint is the 'Refined Steel' imprint - cutlers made much use of imported steel at first, but with Benjamin Huntsman's process of melting blister steel in a crucible the more refined crucible steel (also known as 'cast steel') was made available to cutlers and it dominated Sheffield. Rodgers didn't make their own steel (shear steel) until 1890, and went on to make crucible steel in 1894.
By 1890 Rodgers was so pre-eminent in Sheffield and abroad, and so image-minded that the star and maltese cross and the royal warrant were stamped onto most everything they made, so I would guess at a very much earlier date based on the above info, condensed from Geoffrey Tweedales writings.