The 'Junior' trade name on the rifles was the Model designation of the 900 series before 1898 when they were still with Merwin & Hulbert. After M&H was out of the business and H&A was on it's own the 900 series continued with a few changes (longer front of the frame w/takedown screw underneath instead of on the side being the main difference). The rifles continued to be listed in catalogs as 'New Model Junior Rifle' & 'Junior Model Schuetzen' etc. I've read that the name 'Junior was not placed on the rifle after the company reorganization but your's and others I've seen plainly have the marking on the barrel.
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The Catalog prints show a rear site on the 900 series that looks very much like the one on your rifle. An elevatation adj site fitted into a dovetail. Yours could be a bit newer than the rifle, hard to tell in the photo. The lesser models 800 and 700 series had a simple block w/notch rear site.
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The Lyman Tang Sight is the rear action tang mounted target site used on the Junior Scheutzen model 3922/3932. Here's a pic of a Marbles brand Tang site, this one fits a Savage 99 rifle, but you get the idea. Just a different base to fit your rifle.
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The H&A uses the same site # as used on the Marlin L/A 22 IIRC.
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....and as a very rare option on these rifles,,a double set trigger could be ordered. It was a close coupled set trigger much like the Winchester design. I've seen one H&A rifle with them installed on it.