В этом отрывке есть короткая цитата, которую я потом долго вспоминал.

Because в can take different cases depending on the meaning:

• в + prepositional = in / inside / within
• в + accusative = into / to / for motion toward

Here, the sentence means in this excerpt, so Russian uses the prepositional case:

• в этом отрывке = in this excerpt

Compare:

• в этом отрывке = in this excerpt
• в этот отрывок = into this excerpt

So этом and отрывке are both in the prepositional because the phrase describes location, not movement.

Отрывке is the prepositional singular form of отрывок.

The dictionary form is:

• отрывок = excerpt, passage

After в with the meaning in, a masculine noun like this usually goes into the prepositional:

• отрывок → в отрывке

The adjective/demonstrative also changes to match it:

• этот отрывок
• в этом отрывке

So the whole phrase agrees in masculine singular prepositional.

Yes, есть can often be omitted in present-tense Russian, but here it helps express there is / there exists.

• В этом отрывке есть короткая цитата = There is a short quotation in this excerpt.

Without есть, the sentence would still be understandable:

• В этом отрывке короткая цитата

But that sounds more like there is a short quotation in this excerpt only in a looser, less explicitly existential way, and in some contexts it may feel more like identifying or describing what the excerpt contains. Using есть clearly marks the idea of existence/presence.

Russian adjectives must agree with the noun in gender, number, and case.

The noun цитата is:

• feminine
• singular
• here in the nominative, because it is the thing that exists after есть

So the adjective must match:

• короткий → masculine
• короткая → feminine
• короткая цитата

That is why you see -ая on короткая.

Because которую is the accusative feminine singular form of который, and it refers back to цитата.

The relative clause is:

• которую я потом долго вспоминал

Inside that clause, the quotation is the object of вспоминал:

• I remembered what? → the quotation

Since цитата is feminine singular, который must agree with it, and because it is the direct object, it takes the accusative form:

• nominative: которая
• accusative feminine: которую

So literally it is something like:

• a short quotation, which I later remembered for a long time

Because которую я потом долго вспоминал is a relative clause modifying цитата.

Russian normally sets off this kind of clause with a comma:

• цитата, которую...
• книга, которую...
• человек, который...

This is similar to English:

• the quotation that/which I remembered

Russian punctuation is more consistent here than English: the comma is required.

Вспоминал is the past tense, masculine singular form of the verb вспоминать.

Russian past tense agrees with the subject in gender and number:

• я вспоминал = I remembered / was remembering, if the speaker is male
• я вспоминала = same meaning, if the speaker is female

So this sentence suggests the speaker is male. If the speaker were female, it would be:

• ...которую я потом долго вспоминала.

Because the sentence emphasizes an ongoing or repeated mental process: the speaker kept remembering it for quite a while.

• вспоминать = imperfective
• вспомнить = perfective

Here:

• потом долго вспоминал = later kept recalling it / remembered it for a long time

A perfective verb like вспомнил would usually focus on a single completed act:

• потом вспомнил = later remembered it, managed to recall it

But долго fits naturally with the imperfective, because it describes duration.

Together they mean something like:

• later, for a long time
• afterward, for quite a while

So:

• я потом долго вспоминал = I later kept remembering it for a long time

The adverbs have different roles:

• потом = later, afterward
• долго = for a long time

So the timeline is:

1. there was a quotation in the excerpt
2. afterward, the speaker kept recalling it

Not always. Russian often drops personal pronouns when the verb form already shows the subject.

You could say:

• ...которую потом долго вспоминал.

That can still mean which I later remembered for a long time, especially if the subject is clear from context.

But я is included here for clarity or emphasis. It can make the sentence feel a little more explicit or personal.

Yes, Russian word order is flexible, but the chosen order is natural and neutral.

This order does the following:

• В этом отрывке sets the scene first: in this excerpt
• есть introduces existence: there is
• короткая цитата gives the thing being introduced

So it flows as:

• In this excerpt, there is a short quotation...

Other orders are possible, but they change emphasis. For example:

• Короткая цитата есть в этом отрывке
  This puts more focus on short quotation.
• Есть в этом отрывке короткая цитата...
  This is possible, but less neutral and more marked stylistically.

The original sentence is the most straightforward for ordinary prose.