The image you have posted appears to be an 1863 $2 note (without town overprint) from The Quebec Bank (cat # 620-34-04).
The most recent catalogue says that the only known examples of this note are in Institutional Collections.
The note appears to be in very poor condition and would grade as "Good" at best. Because of its fragile condition and unique status it is worth having it graded and put into a protective slab. The cost to have it graded by BCS is only $15 and is well worth the investment.
Although no catalogue value is given for this due to its unique status it would probably sell at auction for CAD $1000+. I base this on the catalogue value of $1000 given for the same note with town overprint in Good condition. It may sell for considerably more since no notes (up until now) are known to exist in private hands.
Logged
Arthur Richards
Contributor, Charlton Catalogue of Canadian Government Paper Money, 19th, 20th, 21st, 22nd and 29th Edition
Pricing Panel Member, Charlton Catalogue of Canadian Government Paper Money, 21st Edition 2009