There is some academic research on this topic that you can find online. Once person you could contact who has worked with archeological fingerprints on ceramics is warren Barbour at the University of Buffalo.
A possibility is to show them to a police expert. But the prints should be quite complete in order to obtain a reliable result.
What are these clay objects? Are they clay sealings? If they are sealings, I would suggest you, in general, not specifically for finger prints, to consult the book:
M. Frangipane, P. Ferioli, E. Fiandra, R. Laurito, H. Pittman (M. Frangipane ed.), "Arslantepe Cretulae. An Early Centralised Administrative System Before Writing", ‘ARSLANTEPE’ vol. V, Università di Roma La Sapienza, Roma, 2007 (528 pagg. + Catalogue in DVD). ISBN: 88-901701-7-4 (distribution: Arbor Sapientiae, www.arborsapientiae.com – [email protected])
Kewal Krishan, Tanuj Kanchan and Chitrabala Ngangom, 2013.A study of sex differences in fingerprint ridge density in a North Indian young adult population.
Journal of Forensic and Legal Medicine (Impact Factor: 0.99). 05/2013; 20(4):217-22. DOI: 10.1016/j.jflm.2012.09.008
It shows that there is a statistically significant difference in ridge density between fingerprints of young men and women in current day India.
You can take a sample of the fingerprint and stain it with DAPI (a nucleic acid stain). Under UV light, if the fingerprints glow, there are nucleic acids on them.
Send the sample for DNA sequencing and they should be able to tell you whether the samples are male or female.
This will work only if there is a very small chance of cross contamination.
Kamp, Kathryn et al. 1999 Discovering Childhood: Using Fingerprints to Find Children in the Archaeological Record. American Antiquity 64 no. 2 pp 309-315
I'm currently analyzing data on fingerprints from the US Southwest, and expect to have an article on the work soon. I've relied on many of the studies cited above, especially the Kamp article and papers by Miroslav Kralik. Akiva Sanders at UPenn just published this article, which is very similar to my approach:
Interesting paper from John Whittaker. There is strong suspicion that children were making the smallest samian bowls [terra sigillata] as they had small hands. Fingerprints would be a possible means of proof.
The key criterion that I and others have used is ridge breadth, so you need to have enough of a fingerprint to measure that. Articles by Kralik, Sanders, Kamp, and others go into details on how to account for clay shrinkage, ethnicity, etc. I use a stereo microscope with a camera attachment, and I think that's what Sanders used as well, to take calibrated snapshots of the microscope field that can be then measured. I hope to have an article out on this soon, but check out the other authors referenced in this thread.
As for Gaulish terra sigillata, I'm not aware that its [very frequent] fingerprints have ever been analysed. John Whittaker and others referred to an article by Kathryn Kamp which I found: https://www.academia.edu/8531566/Where_Have_All_the_Children_Gone_The_Archaeology_of_Childhood
That children have made the small ceramic utensils found in excavations, I have seen already in imported Late Bronze Cypriote pottery found in Akko, Israel.
Concerning measuring the width of fingerprints taking into account the shrinkage of clay, we should be careful because every clay has a different shrinking characteristic depending on the amount of water, hygroscopic water and mineral water (yes, three types of water) on the one hand and the firing temperature of a potter's kiln on the other.