Submit being called twice

e.preventDefault(); will prevent form from submitting, but whoever is submitting is button , once per default behavior, and again because of the eventListener you placed on it.

You can handle this in the following ways:

$("#frmTeste").on('submit', function (e) {
    e.preventDefault();
    alert('teste');
    return false;
});

$("#btnTeste1").on('click', function (e) {
    e.preventDefault();
    $("#frmTeste").submit();
});

$("#btnTeste2").on('click', function () {
    $("#frmTeste").submit();
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.0.0/jquery.min.js"></script><formid="frmTeste">
    <input type="text" name="teste">
    <button id="btnTeste1">
        Cadastrar1
    </button>
    <button id="btnTeste2" type="button">
        Cadastrar2
    </button>
    <button id="btnTeste3">
        Cadastrar3
    </button>     
</form>

  

even using preventDefault (); and return false; submit is running twice.

Notice the comments:

$("#frmTeste").on('submit', function (e) { // AO SUBMIT
    e.preventDefault(); // NÃO EXECUTAR O PADRÃO (SUBMIT) ????
    alert('teste'); 
    return false;
});

$("#btnTeste").on('click', function () { // AO CLICAR EM #btnTeste
    $("#frmTeste").submit(); // SUBMIT NO FORMULÁRIO
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.0.0/jquery.min.js"></script><formid="frmTeste">
    <input type="text" name="teste">
    <button id="btnTeste">
        Cadastrar
    </button>
</form>

For this to work, you should put preventDefault() in the block that captures the click of the button, not the block that submits the form:

    $("#btnTeste").on('click', function (e) {
        e.preventDefault();
        $("#frmTeste").submit();
    });

But, still, this is wrong! You can simply put a button with type="submit" that would give it!

Uncovered the error in the code, let's get a solution:

  

intercept the submit event, cancel it and via Ajax, perform the request

This, perhaps, is a solution to your question:

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.0.0/jquery.min.js"></script><formid="frmTeste" action="" method="post">
    <input type="text" name="teste">
    <button id="btnTeste">
        Cadastrar
    </button>
</form>

<script type="text/javascript">
    $('#btnTeste').on('click', function(e){
        e.preventDefault(); // NÃO EXECUTA O SUBMIT, COMO ACONTECE NORMALMENTE
        e.stopPropagation(); // IMPEDE QUE SEJAM EXECUTADOS OUTROS HANDLERS
        $.ajax({
            url: $('#frmTeste').attr('action'),
            method: $('#frmTeste').attr('method'),
            data: $('#frmTeste').serialize(),
            beforeSend: function(){
                // TUDO QUE ACONTECE ANTES DE EXECUTAR A REQUISIÇÃO AJAX
            },
            success: function(){
                // TUDO QUE ACONTECE APÓS A REQUISIÇÃO (RESPOSTA DA REQUISIÇÃO)
                // SE FOR EXIBIR ALGO REFERENTE A RESPOSTA, DEVE ADICIONAR O PARÂMETRO NA function(<parametro>){ //...
            },
            error: function(){
                // TUDO QUE ACONTECE CASO OCORRA ALGUM ERRO NA REQUISIÇÃO
            }
        });
    });
</script>

I have not tested the code, but I usually use jQuery 1.2 . I believe that in the version you are using you should reformulate the ajax part with .done / .error ...