Amped Raptor

First strike
When this creature enters, you get {E}{E} (two energy counters). Then if you cast it from your hand, exile cards from the top of your library until you exile a nonland card. You may cast that card by paying an amount of {E} equal to its mana value rather than paying its mana cost.

Modern Horizons 3

First strike
When Amped Raptor enters the battlefield, you get {E}{E} (two energy counters). Then if you cast it from your hand, exile cards from the top of your library until you exile a nonland card. You may cast that card by paying an amount of {E} equal to its mana value rather than paying its mana cost.

Any land cards exiled with Amped Raptor's triggered ability will remain in exile. If you choose not to cast the exiled nonland card (either because you don't have enough {E} or you just don't want to), that card will remain in exile as well.

Energy counters are a kind of counter that a player may have. They're not associated with any specific permanents.

Energy counters aren't mana. They don't go away as steps, phases, and turns end, and effects that add mana "of any type" can't give you energy counters.

If a spell or ability with one or more targets states that you "may pay" some amount of {E}, and each permanent that it targets has become an illegal target, the spell or ability won't resolve. You can't pay any {E} even if you want to.

If an effect says you get one or more {E}, you get that many energy counters. To pay one or more {E}, you lose that many energy counters. You can't pay more energy counters than you have. Any effects that interact with counters a player gets, has, or loses can interact with energy counters.

If you cast a spell for another cost "rather than paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the spell has any mandatory additional costs, those must be paid to cast it.

Keep track of how many energy counters each player has. Potential ways to track this include writing theme down on paper or using dice, but any method that is clear and mutually agreeable is fine. (At higher levels of tournament play, dice may not be allowed for tracking counters that players have.)

Some spells and abilities that give you {E} may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won't resolve. You won't get any {E}.

Some triggered abilities state that you "may pay" a certain amount of {E}. You can't pay that amount multiple times to multiply the effect. You simply choose whether or not to pay that amount of {E} as the ability resolves.

Some triggered abilities that state that you "may pay" a certain amount of {E} describe an effect that happens "If you do." In that case, no player may take actions to try to stop the ability's effect after you make your choice. If the payment is followed by the phrase "When you do," then you'll choose any targets for that reflexive triggered ability and put it on the stack before players can take actions.

You choose whether or not to cast the exiled nonland card as Amped Raptor's triggered ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.