The document by LTG Bogdanovich I've found translated from Russian into English by Mark Conrad here: link indicate that each battalion had a small company of 28 men [with another 28 men trained as replacements but serving in a line company] with a Liege rifle [Rifle battalions had rifled 7-line [0.70 caliber] Liège "shtutser" weapons.
In each infantry battalion there were 2 non-commissioned officers and 24 privates armed with these shtutser rifles, and they were called shtutsernye [riflemen] (14).], which seems to be an old-pattern rifle of the Napoleonic era, likely modified with the percussion cap – open to correction, here.
"These men formed up in the rear line of non-commissioned officers, three behind each platoon. They were called out into a skirmish line at a special signal. In addition to them, there were also 24 replacement riflemen in a battalion, trained to fire the shtutser but not equipped with one. They were numbered along with the ordinary majority of the unit's soldiers."
Interestingly, the Russian General states that the close order of the Russian infantry battalions is NOT because the Russian army was backwards and Napoleonic, but that the close order was necessitated by the tactics of the Turks, who used thousands of irregular bashi-bazooks and could easily envelope any small part of a Russian battalion that was operating independantly. Skirmishers were therefore used only in heavy terrain and with the battalion nearby in support.
"The headquarters of the commander of the 4th and 5th Infantry Corps prepared special instructions for operations against the Turks. These were titled Instructions for Battle Against Turks, and were approved by Highest Authority on 20 July, 1853. Copies were sent to all column commanders.
The basis of these instructions were rules observed by Prince Paskevich in his wars against the Persians and Turks. The main idea underlying all these rules was the desire to give all military formations the greatest possible cohesiveness and mass, in order to withstand the Turkish cavalry's headlong and disordered attacks and the infantry's huge, unorganized masses, which always moved forward to envelop the attacked units from both sides.
To achieve this, our side avoided movements in open order as much as possible. Even on ground that was uneven or covered with tall bushes, we covered a solid front not with a skirmish line, but with rifle platoons drawn up in close formation or with company columns. Riflemen were sent out in open order only in the mostly heavily wooded terrain. The cavalry was likewise not permitted to send out flankers, whose place was taken by close-order platoons or half-squadrons."