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You can try:

public function initContent()
{
        $this->content = $this->context->smarty->fetch(_PS_MODULE_DIR_.$this->module->name.'/views/templates/admin/edit.tpl');
        parent::initContent();
}

Try adding this method, in your controller:

public function setTemplate($template, $params = array(), $locale = null)
    {
        if (strpos($template, 'module:') === 0) {
            $this->template = $template;
        } else {
            parent::setTemplate($template, $params, $locale);
        }
    }

L.E. Works for front controller.

for admin controller, you can try:

public function initContent()
{
        $this->content = $this->context->smarty->fetch(_PS_MODULE_DIR_.$this->module->name.'/views/templates/admin/edit.tpl');
        parent::initContent();
}

Try adding this method, in your controller:

public function setTemplate($template, $params = array(), $locale = null)
    {
        if (strpos($template, 'module:') === 0) {
            $this->template = $template;
        } else {
            parent::setTemplate($template, $params, $locale);
        }
    }

L.E. Works for front controller.