Learn Hardcore Turkish: Annem, “erken yat” diye beni uyardı. - My mother warned me, “Go to bed early.”

diye links the quoted words to the main verb and means roughly “saying/with the words.” In Annem, erken yat diye beni uyardı, it tells us that the warning consisted of the words erken yat. It is the standard connector after many verbs (uyarmak, bağırmak, yazmak, düşünmek, sormak, vb.).
You could also use diyerek with a similar meaning of “by saying”: Annem, erken yat diyerek beni uyardı. Dropping diye removes the content of the warning: Annem beni uyardı.

Why is it beni and not bana?

Because uyarmak (“to warn”) takes a direct object in the accusative for the person being warned. Beni is the accusative form of ben.

Correct: Annem beni uyardı.
Incorrect: Annem bana uyardı.
By contrast, verbs like söylemek and demek take the dative for the person addressed: Annem bana söyledi/dedi.

What form is yat, and why not yatmak?

Yat is the 2nd person singular imperative of yatmak (“to lie down; go to bed”). Inside the quoted words, a direct command is intended, so the imperative is used: erken yat = “go to bed early.”
Yatmak is just the dictionary form (“to go to bed”) and is not used for giving a command.

Could it be uyu instead of yat?

You can say erken uyu (“sleep early”), but erken yat is more common when telling someone to go to bed.

Yat focuses on going to bed/lying down.
Uyu focuses on actually sleeping.
A parent typically says erken yat at bedtime.

Why is the adverb before the verb? Can I say yat erken?

In Turkish, adverbs normally come before the verb, so erken yat is the natural order. Yat erken is ungrammatical/very odd.
You may also hear erkenden (“earlier than usual”): erkenden yat adds a nuance of “earlier than you normally would.”

Can I use dedi instead of diye?

If you switch to dedi, you should use it as the main verb of saying: Annem, erken yat, dedi.
But when your main verb is something else (here, uyardı), you attach the quoted content with diye: Annem, erken yat diye beni uyardı.
You can, of course, coordinate: Annem, erken yat, dedi ve beni uyardı.

Why is there a comma after Annem, and should Erken be capitalized inside the quote?

Turkish punctuation normally sets off a direct quotation with a comma before the opening quote, so Annem, … is standard.
As for capitalization: if what’s quoted is a full sentence (here, an imperative), capitalizing the first word is common practice (e.g., Erken yat). In informal writing you’ll also see lower-case. Both appear in real usage.

What does the -m in annem mean?

Annem = anne (mother) + first-person singular possessive -m (“my”). So annem means “my mother.”
If it were an object, you’d add accusative: annemi (“my mother” as a direct object).

Is the word order fixed? Can I move beni or the quoted part?

Word order is flexible. All of these are fine, with slight differences in emphasis:

Annem, erken yat diye beni uyardı. (neutral)
Annem beni erken yat diye uyardı. (places the person earlier)
Beni annem erken yat diye uyardı. (focus on “me”)
Erken yat diye annem beni uyardı. (fronts the quoted content)

How would I say this in indirect speech (no direct words)?

Common options:

With söylemek + nominalization: Annem bana erken yatmamı söyledi.
With gerekmek: Annem, erken yatmam gerektiğini söyledi.
With uyarmak (topic-based): Annem, erken yatmam konusunda beni uyardı.
The first two sound more like telling/advising; uyarmak has a “warning/admonishing” flavor.

What tense is uyardı?

Uyardı is simple past (the -DI past).

uyarıyor = is warning (present progressive)
uyarır = warns/would warn (habitual/general)
uyarmış = apparently/it seems she warned (reportative/inferential)

Can I omit beni?

Grammatically, yes: Annem, erken yat diye uyardı. The person warned would then be understood from context (often “me” in a typical family scene). Including beni makes it explicit and removes ambiguity.

Does diye only attach direct quotes?

No. Diye also introduces purpose/reason or reported thought, often with a finite or nominalized clause:

Purpose: Ertesi gün dinç olayım diye erken yattım. (“I went to bed early so that I’d be fresh the next day.”)
Reported thought: Şaka yapıyor diye güldüm. (“I laughed, thinking he was joking.”)

How would I warn in the negative?

Use the negative imperative inside the quoted part: geç yatma (“don’t go to bed late”), telefonla oynama (“don’t play with the phone”).
Example with this structure: Annem, geç yatma diye beni uyardı.