As you are using jQuery create elements using it and also bind event using it. Here in example I have used .data() to store arbitrary value which can be fetched in the click handler
var a = $('<a>Click</a>')
.data('parameter1', parameter1)
.data('parameter2', parameter2)
.on('click', function(){
var parameter1 = $(this).data('parameter1');
var parameter2 = $(this).data('parameter2');
my_function(parameter1, parameter2)
});
For immediate problem, you need to escape quotes properly
var a = '<a onclick="my_function(\''+ parameter1 + '\',\'' parameter2 + '\')">Click</a>';
As per comment parameter1 is a number you don't need to wrap it.
var a = '<a onclick="my_function('+ parameter1 + ',\'' parameter2 + '\')">Click</a>';