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Across many media, Amy has displayed a lot of abilities, some more curious than others. Some appear psychic or magical in nature, while in another case she harnessed chaos energy. I’ll be covering the psychic part first, pulling mainly from the games continuity with a reference or two to the archie comics.
Officially, Amy is listed to be "slightly psychic" but considering how many of us tend to use Silver as a benchmark for how typical psychic abilities operate in the games ( flying, moving things, teleportation, freezing opponents, etc ), that leaves a lot of wiggle room for Amy.

Psionic / psychic abilities are reliant on manipulating internal mental energies to perform effects. For example, it can manifest as psychokinesis ( any ability that involves using the mind to manipulate something ) or extrasensory perception aka ESP ( someone’s senses expanding to the point they can "see" more of the world, like seeing things as they happen miles away, or seeing the future or past ). Silver is skilled in the former, while Amy mostly specializes in the latter.
Amy's not super overt about her psychic powers like Silver is. Mostly due to the fact she isn't fully aware of them and / or regards most of them as magical or mystical practices rather than psychic. She doesn't really apply them to fights but they are still very much present.
Clairvoyance - Amy has the ability to receive information about a person or an object even if she has never directly seen them before. Her most prominent and frequent example is her tarot cards. Using her deck, Amy has been able to deduce the general location of someone she's searching for and predict / "foresee" fate to a certain degree through fortune telling. It's not the same as having future vision. It's difficult for her to divine her own fortune, but Amy's readings for others have gotten rather accurate over time. ESP.
Heightened Intuition - Typically described as getting a "feeling" about certain things or people, seeing into one's very soul or detecting certain danger. Cream notation of Amy's "Sonic Radar" during Rush is a form of this. Aside from Sonic, Amy can "feel" where a person has been, like how she pointed out that she sensed Chocola and Froggy were likely in Dr. Eggman's Rail Canyon base during Heroes. ESP.
Premonitions - "I still dream that Sonic is with us. Do you think he might be...?" Despite Sonic being presumed dead in Forces, through her dreams Amy appears to be hinting at Sonic still being alive and then he’s eventually revealed to be. Users of divination often pay attention to their dreams, since they can provide enlightenment in strange ways. Basically vague prophetic dreams, but I imagine she only gets these once in a blue moon. ESP.
Invisibility - By concentrating, Amy emits a pink energy that envelops her. Once the energy has been focused, several transparent rings move up and down her body which turn her fully invisible for fifteen seconds. In this, I think she is essentially bending light around herself. This randomly showed up in Sonic '06, but given the introduction of Silver and Sega leaning into psychic powers, this can finally give it more context. Psychokinesis.
Amy Flash - It's an attack that freezes opponents for a brief duration of time, completely immobilizing them. It looks like a type of temporary paralysis, seen in SA2:Battle. My Amy can do this from a distance, but she has to concentrate and the person must be in her line of sight. Psychokinesis.
Some additional minor points that hint further at psychic powers is that (Archie) Amy has meditated in an effort to increase her fighting power, and game Amy is continually noted to have the dowsing ability. Not much detail is known about her specific usage of dowsing ( aside from her having excellent skills in it and that it's separate from her cartomancy ), but it's one of her methods of repeatedly tracking down Sonic no matter where he is in the world. Dowsing typically falls under ESP used to locate something.
The series barely acknowledges a thing about family on the best of days, but even then it's impressive how Amy's parents never get so much as a mention ( in other material like the archie comics, she has a cousin in that continuity but her parents don't get talked about like at all ). There's a myraid of possible reasons as to why that's the case so until further notice I'll assume they aren't in the picture whatsoever.
Amy has no memory of her parents. She has no idea if she's even met them and doesn't see the point on lingering on something like that. As far as she's concerned she's an orphan, thus she finds it unnecessary to ever bring up the subject.
Heritage wise, on the paternal side her father had a knack for psychic things too. I believe all this mysticism stems from a distant ancestor, whom had an untapped connection to chaos energy. On the maternal side, her grandmother was actually an echidna. One of the few that remained on land after the whole Chaos incident and Angel Island being raised into the sky. While mostly exhibiting hedgehog traits, having some echidna genes explains a few things like her coloring, nose shape, and partially where her insane strength comes from.