Although citations to cap numerals/letters appear in some southern states' regs, the studio photographic evidence quite convincingly supports that the usage of such devices among Confederate troops was the exception rather than the rule, and tended to appear earlier in the war. Even in photos wherein appear several members of the same unit, some fellows may have insignia while others do not, and the specific motif is apt to differ among those wearing any. Far more the case than among federal enlisted men, Johnnies tended to care little for regulations and opted to "dress" their headgear, if at all, per personal preferences. In some identified images, the letters are actually the man's initials, although this practice was surely a rarity.
As to your photo, the immediate top-of-mind candidate for the "SCI" would be "South Carolina Infantry." If the image appears to date from 1861, however, it is also possible that the company nickname was being referenced, such as in "Smith Creek Invincibles." While immensely more common among Yanks, the use of "I" for "infantry" in such insignia is known in Confederate images, as is also the abbreviation of the informal company name. So, while the Tennessee attribution would be at dissonance with the South Carolina interpretation, a company designation for the former state is possible. If feasible to send via e-mail, a copy of the image could be greatly helpful, thus please feel free to post or send one.
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