Quiero dejar mi mochila junto a la puerta.

Because after querer when you mean to want to do something, Spanish uses an infinitive.

• quiero = I want
• dejar = to leave / to put / to set down

So:

• Quiero dejar = I want to leave / put down

You do not use a second conjugated verb after quiero in this structure.

More examples:

• Quiero comer = I want to eat
• Quiero salir = I want to go out

Here dejar means something like to leave, to put down, or to set somewhere.

In this sentence, it does not mean to abandon forever. It just means placing the backpack somewhere.

Depending on context, dejar can mean different things:

• leave something somewhere
• let / allow someone to do something
• stop / quit something

Examples:

• Voy a dejar las llaves en la mesa. = I’m going to leave the keys on the table.
• Mis padres no me dejan salir. = My parents don’t let me go out.
• Dejó de fumar. = He/She quit smoking.

So in your sentence, dejar is the everyday verb for putting the backpack somewhere and leaving it there.

Because the normal, neutral way to say my backpack in Spanish is to put the possessive before the noun:

• mi mochila = my backpack

Spanish does have forms like la mochila mía, but they are more emphatic, contrastive, or stylistically marked.

For example:

• Quiero dejar mi mochila... = normal
• Quiero dejar la mochila mía, no la tuya. = I want to leave my backpack, not yours.

So for everyday use, mi mochila is the standard choice.

Because Spanish usually does not use an article with a possessive adjective in this position.

So you say:

• mi mochila
• tu libro
• su casa

Not:

• la mi mochila ❌

This is different from English in a way, because English also uses just my backpack, but learners sometimes expect Spanish to add an article. In this structure, it does not.

Junto a means next to, beside, or by.

It is a fixed expression:

• junto a la puerta = next to the door

The a is part of the expression junto a. You should learn it as a unit.

Compare:

• junto a la ventana = next to the window
• junto al coche = next to the car

Notice that a + el = al:

• junto al coche
• but junto a la puerta

Yes. Both are natural.

• junto a la puerta = next to / beside the door
• al lado de la puerta = next to / at the side of the door

In many situations they mean almost the same thing. Junto a can sound a little more compact or slightly more formal in some contexts, while al lado de is also extremely common and very natural.

So these are both fine:

• Quiero dejar mi mochila junto a la puerta.
• Quiero dejar mi mochila al lado de la puerta.

Spanish usually uses the definite article with specific, identifiable things much more often than English does.

So:

• junto a la puerta = by the door

In English, the is also used here, so this part matches English quite well. But in Spanish, using the article is very normal with places and objects when both speaker and listener can identify them.

For example:

• Está en la cocina. = It’s in the kitchen.
• Deja el libro en la mesa. = Leave the book on the table.

Yes, but the original order is the most neutral and natural.

Standard order:

• Quiero dejar mi mochila junto a la puerta.

Other possible orders:

• Quiero dejar junto a la puerta mi mochila.
• Mi mochila quiero dejarla junto a la puerta. — more marked or emphatic

Spanish word order is more flexible than English, but that does not mean all orders sound equally natural. The original sentence is the safest everyday version.

Yes, often you can, but the nuance is slightly different.

• poner = to put
• dejar = to leave / leave placed

Compare:

• Quiero poner mi mochila junto a la puerta.
• Quiero dejar mi mochila junto a la puerta.

Both can work.
But dejar often suggests putting it there and leaving it there, which fits very well with a backpack. Poner focuses more simply on the action of placing it.

In many real situations, both are natural.

In standard Spanish pronunciation, quiero sounds roughly like KYEH-roh.

A few useful points:

• qu before i/e sounds like a hard k
• ie in quiero forms a diphthong, so it is said together
• the r in quiero is a single tapped r, not the strong rolled rr

So:

• quiero ≈ KYEH-roh

Also:

• dejar in Spain is roughly de-HAR
• mochila ≈ mo-CHEE-la
• puerta ≈ PWER-ta

It is perfectly correct, but by itself it can sound a bit plain if you are asking permission in a formal situation.

If you are simply stating your intention, it is fine:

• Quiero dejar mi mochila junto a la puerta.

But if you want to sound more polite in Spain, you might say:

• ¿Puedo dejar mi mochila junto a la puerta? = Can I leave my backpack by the door?
• Querría dejar mi mochila junto a la puerta. = I’d like to leave my backpack by the door.
• ¿Le importa si dejo mi mochila junto a la puerta? = Do you mind if I leave my backpack by the door?

So the original sentence is grammatically good, but context determines whether it feels polite enough.