There is very little information that is easily found on the subject. So, it is hardly authoritative. However, it looks like some can. The turtle seems to show the strongest evidence:
They certainly do have preferences for different people, and I’ve experienced it myself. Iguanas and turtles exhibit different personalities per reptile, so some may be social, some back be laid back, some may be aggressive, and some may be picky on who handles it.
I remember having a turtle as a class pet. This turtle seemed like it really liked it’s original owner, the teacher. If she picked it up, the turtle would just look around aimlessly, and show signs of pleasure when their head of shell was being stroked. But when we tried to touch them or pick him up, he would flail endlessly.
Apparently some classes of animal respond to stress with an increase of body temperature, which may be, obviously, used to test their emotional state:
Theres something called emotional fever.
Experiments done with mammals, birds, amphibians, and reptiles show that they respond to stress by exhibiting an increase in their body temperature, usually by 1 or 2 Celsius. This usually gives scientists a good sign that they are sentient anyways. But it’s harder to do this with fish.
By the way, “herpetology” is the study of reptiles and amphibians. A “herp” is someone who is involved with them.
The featured image is of a terrified turtle I rescued who was sitting on the lane line, between lanes, with head retracted, during rush hour, on a busy road.