I started to answer this question and realized that I'm going to need some clarification of terms. So technically the definition of a fetish is "a form of sexual desire in which gratification is linked to an abnormal degree to a particular object, item of clothing, part of the body, etc.". Finding evidence for this is really problematic because the ancients simply did not define or think about their sexuality in the same ways that we do. I'll look around a bit more, but right now I can't think of anything that suggests a specific fixation like a foot fetish. I regrettably googled what the most common fetishes are and of the things listed the best attested in the ancient world are probably cross-dressing and domination. However, these are practiced in a very different way and for very different reasons. For one thing, the ancients had completely different sexual categories and no concept of consent so the whole sexual dynamic was very different.
But I also considered that perhaps you're asking about fetish in a less specific sense. There are a number of sexual practices that are acknowledged to exist, but considered taboo or unusual. The ancients also engaged in sexual activities that our society would generally consider to be a fetish (or kink or perversion depending on how judgy you're feeling), but were not considered to be unusual.
As an example, let’s start with one difference in ancient sexuality that everyone knows about – the ancients were way more into kids than we are.
On the female side of the equation, girls were seen as marriageable and sexually desirable at menarche, generally a much younger age than we as a society consider acceptable. Ancient Greeks also practiced pederasty – as you can see here – and the Romans continued the practice. In fact, one of the best sculpturally attested individuals of the ancient world is Antinoos, Emperor Hadrian’s boy beloved. I wouldn’t consider pederasty a fetish (or kink or what have you) because it was mostly considered to be mainstream acceptable, but there were exceptions and if we’re considering attested practices considered to be outside of mainstream acceptance than the parameters set us up for another practice – that of men trying to appear as teenagers.
Now we don’t have any evidence to suggest that grown men were dressing up as babies, but we do have ample evidence for both the Greek and Roman period – including from the beloved philosopher Plato, no less! – of men purposely trying to look like they were still young teenagers (plucking body hair, speaking in high pitched voices). There is a kind of logic to this. While pederasty was idealized, homosexual relations between two adult men was considered shameful, being the “beloved” (that is the younger, submissive partner in the relationship) was considered a phase that one would grow out of. As an adult man, being accused of passivity was a serious insult, as might be seen in the infamous Catullus 16 or frequently in the work of Martial (eg. 3.71). So in this example, we have an attested practice where certain elements would be considered a fetish under the modern definition, but the normal ancient practice is itself pretty unusual to modern ideas of sexuality.
On a related note, what exactly is the deal with the tradition that Aristotle and Phyllis had a whole kinky pony thing going on?