There are several ways that the two major parties restrict third party access to presidential elections, including challenging signatures for ballot access and:

Other than signature requirements the most common way that states restrict third party ballot access is by requiring third parties to have met a vote threshold in prior general elections. So, for example, if a party wishes to run a candidate for president but did not have any candidates in a particular state during the prior midterm, then the third party might not be granted access to the ballot.