Is there a difference between "Ẓ" and "ẓ"?
After a thorough review of several texts and online sources I cannot find any evidence of a significant difference in the usage between the uppercase and the lowercase Z with a diacritic dot below the letter. I think the context is pertinent in discovering the intent of the usage (Can you share the textual reference?). But lack of evidence is not sufficient to rule out the possibility of a difference. Here is what I have found so far (I will continue once I get a contextual point of reference):
The underdot is a common transliteration element used in different languages whose appearance in a Chinese language volume appears to indicate usage of the term from an older romanisation system. Wikitionary classifies the symbol as Translingual (which implies its usage as a phonetic code). The current library of Congress romanisation does not include this term and does provide references to other sources for disambiguation of conflicting text.
A wikipedia article on obsolete and non-standard IPA symbols indicate:
Several symbols indicating secondary articulation have been dropped
altogether, with the idea that such things should be indicated with
diacritics: ʮ for z̩ʷ is one
The IPA symbol chart appears to have a [related?] symbol (note the glyph used in the symbol may be a font variant) described as "Voiced labial-palatal approximate," however the underdot shown on IPA is described as "Voiceless". I've reviewed the Chinese phonetic transcription systems listed on Omniglot without finding these symbols and several offline books (again without success). As a student of both Cantonese and Mandarin, I've even taken a look at the Sydney Lau, Wade-Giles, Meyer-Wempe, and Yale romanisations systems. I do have one other dictionary (which is currently missing) that may have further references.
Checking on Chinese Notes revealed little new insight on the origin/behaviour of this symbol. Nciku and Zdic (surprisingly) also came up empty while researching this symbol. Pinyin Info reviews several romanisation systems. At this point I have not been able to conclude that the variance is insignificant and require further information to continue.
Other texts evaluated include:
Chen, J., & Simms, E.G. (1992). A Practical English-Chinese Pronouncing Dictionary
McNaughton, W., & Li, Y. (1999). Reading & Writing Chinese: Traditional Character Edition, A Comprehensive Guide to the Chinese Writing System
Liu,Y.H, Yao, T.C., Bi, N.P., & Ge, L.Y. (2006) Integrated Chinese - Traditional & Simplified Character Edition - Workbook
Liu,Y.H, Yao, T.C., Bi, N.P., & Ge, L.Y. (2006) Integrated Chinese - Traditional & Simplified Character Edition - Textbook
Liu,Y.H, Yao, T.C. Bi, N.P., & Ge, L.Y. (2006) Integrated Chinese - Traditional & Simplified Character Edition - Character book
Lau, S. (1972) Elementary Cantonese
Lau, S. (1972) Intermediate Cantonese