How to get the value of a TD?

Try this:

PHP:

<?php

 require_once('acessabanco.php');

 $objDb = new db();
 $link = $objDb->conecta_banco();

 $sql = "SELECT p.sequencia codigo,
                p.nome_completo nome, 
                c.data_nascimento data, 
                t.celular_1 celular
           FROM pessoas p, 
                clientes c, 
                telefones t 
          WHERE p.sequencia = t.cod_pessoa 
            AND c.cod_pessoa = p.sequencia";
 $exec = mysqli_query($link, $sql);     
 if ($exec){
    while ($clientes = mysqli_fetch_array($exec)){
        echo('<tr><td id="sequencia" >' . $clientes['codigo'] . '</td>
              <td>' . $clientes['nome'] . '</td>
              <td>' . $clientes['data'] . '</td>
              <td>' . $clientes['celular'] . '</td>
              <td><button type="button"  id="'.$clientes["codigo"].'" class="btn_sequencia btn btn-primary btn-sm">Small button</button></td>
              </tr>');
    }
}
?>

jQuery:

$(document).ready(function () { 

    $(".btn_sequencia").on('click', function(){
        alert($(this).attr('id'));
    });

    $('#content').css('display', 'none');

    $.ajax({
        url: 'php/lista_clientes.php',
        type: 'post',
        success: function (data) {
            $("#carrega_pag").append(data);
        }
    });

});

Test code:

$(document).ready(function () { 

    $(".btn_sequencia").on('click', function(){
        alert($(this).attr('id'));
    });

    $('#content').css('display', 'none');

    $.ajax({
        url: 'php/lista_clientes.php',
        type: 'post',
        success: function (data) {
            $("#carrega_pag").append(data);
        }
    });

});

<script src="https://code.jquery.com/jquery-1.12.4.min.js"></script><tableclass="table table-hover">
    <thead>
        <tr>
            <th>Código</th>
            <th>Nome Completo</th>
            <th>Data de Nascimento</th>
            <th>Celular</th>
            <th>Opções</th>
        </tr>
    </thead>
    <tbody id ="carrega_pag">
        <tr>
            <td id="sequencia">1</td>
            <td>Joao</td>
            <td>11/11/2017</td>
            <td>99999-9999</td>
            <td><button type="button" id="1" class="btn_sequencia btn btn-primary btn-sm">Small button</button></td>
        </tr>
        <tr>
            <td id="sequencia">2</td>
            <td>Maria</td>
            <td>11/11/2017</td>
            <td>99999-9999</td>
            <td><button type="button" id="2" class="btn_sequencia btn btn-primary btn-sm">Small button</button></td>
        </tr>
    </tbody>
</table>

You need to delegate to new elements returned by Ajax, and use the .on('click'... selector to capture the text of the first% of the clicked button's line.

The code looks like this:

$(document).ready(function () { 

   $('#carrega_pag').on('click',".btn_sequencia", function(){
        alert($(this).closest('tr').find('td').first().text().trim());
    });

   $('#content').css('display', 'none');

   $.ajax({
      url: 'conecta.php',
      type: 'post',
      success: function (data) {
         $("#carrega_pag").append(data);
      }
   });

});