The following variations are all correct. They all mean the same thing:

Is it a Shakespeare quote? (Using his name as an attributive noun.)

 

Is it a Shakespearean quote? (This is the adjective form.)

 

Does that quote come from Shakespeare?

If you had a few quotes to choose from (such as one from the King James Bible, one from Milton, and one from Shakespeare), it would be appropriate to ask "Is it Shakespeare's quote?" In this usage, the possessive is used to indicate the particular quote. This makes the indefinite article "a" redundant. It is incorrect to ask "Is it a Shakespeare's quote?"

By the way, Shakspere could spell his own name... several different ways.

The following variations are all correct. They all mean the same thing:

Is it a Shakespeare quote? (Using his name as an attributive noun.)

Is it a Shakespearean quote? (This is the adjective form.)

Does that quote come from Shakespeare?

If you had a few quotes to choose from (such as one from the King James Bible, one from Milton, and one from Shakespeare), it would be appropriate to ask "Is it Shakespeare's quote?" In this usage, the possessive is used to indicate the particular quote. This makes the indefinite article "a" redundant. It is incorrect to ask "Is it a Shakespeare's quote?"

By the way, Shakspere could spell his own name... several different ways.

The following variations are all correct:

Is it a Shakespeare quote? (Using his name as an attributive noun.)

Is it a Shakespearean quote? (This is the adjective form.)

Does that quote come from Shakespeare?

By the way, Shakespeare could spell his own name... several different ways.

The following variations are all correct. They all mean the same thing:

Is it a Shakespeare quote? (Using his name as an attributive noun.)

Is it a Shakespearean quote? (This is the adjective form.)

Does that quote come from Shakespeare?

If you had a few quotes to choose from (such as one from the King James Bible, one from Milton, and one from Shakespeare), it would be appropriate to ask "Is it Shakespeare's quote?" In this usage, the possessive is used to indicate the particular quote. This makes the indefinite article "a" redundant. It is incorrect to ask "Is it a Shakespeare's quote?"

By the way, Shakspere could spell his own name... several different ways.