I filed to apply my return to next years tax return and I still have not recieved my third stimulus. Does filing this way effect me recieving my stimulus?

No, it doesn't.  The IRS is sending out Stimulus #3 payments in batches, and will take a few weeks to complete them all.  This one comes to you separately (and automatically), not as part of your 2020 tax refund.  You can check the status here:

Get My Payment | Internal Revenue Service (irs.gov)

SweetieJean is correct.

No, applying your current year refund to next year does not cause a delay in processing your return/stimulus.

• Per IRS: They have around 12 million tax returns that have been caught in a processing backlog created by the pandemic, which shut down the IRS for a time. Americans should see their refunds in the coming months. "We would hope to be through this backlog by the summer," said IRS Commissioner Charles Rettig.

Note: The stimulus payments are not taxable income to you.