Remington did indeed make a 1901 Rolling Block Target Pistol (see Flayderman`s Guide to Antique American Firearms). And they did indeed make them in, among other calibers, .44 S & W. However, from what follows, you will understand that I am not sure if your example is actuallya Remington product.
Unfortunately you did not say WHERE the markings are, hence my use of the word "typically" below.
Markings: Belgian obelisk proof mark is the "perron", the old city seal of Liege, where Belgian guns and barrels were proofed. Typically found on the chamber/action body.
E/LG/star is NOT
British
. It is the Belgian proof mark, the letters ELG being derived from Epreuve Liege (Liege proof). The form E over LG over star, all in an oval, is in fact a black-powder proof mark for a standard load. Typically found on the barrel. If there was a crown above the oval his would indicate a proof with an excess load. Used since 1811, so not much help with dating.
Crown over JA&C is most likley the manufacture's initials, JA&C(ompagnie).
Compagnie is otherwise usually abbreviated to Cie (similar to English Co.)
There was a complete dynasty in 19th century Liege with the name Ancion, stretching from 1789 to 1935.
In 1866 JULES and ALFRED ancion set up J. Ancion & Cie, so my guess is:
A Belgian copy of the Remington Rolling Block Target pistol, probably caliber .44 S & W, made post-1866 by a reputable firm, and therefore quite possibly under license from Remington.