You need to use collections for that:

$messages = $objectManager->create('Custom\Module\Model\ResourceModel\Messages\Collection')->addFieldToFilter('posts_id', $this->getRequest()->getParam('id'));

This is assuming you have created a collection resource model for your Messages entity.

NB: please try to avoid using the Object Manager directly

Instead you can inject the collection class in your constructor:

protected $_messagesCollection;

public function __construct(
    ...
    \Custom\Module\Model\ResourceModel\Messages\Collection $messagesCollection,
    ...)
{
    ...
    $this->_messagesCollection = $messagesCollection;
}

And then you can use your variable directly in your code:

$messages = $this->_messagesCollection->addFieldToFilter('posts_id', $this->getRequest()->getParam('id'));

You need to use collections for that:

$messages = $objectManager->create('Custom\Module\Model\ResourceModel\Messages\Collection')->addFieldToFilter('posts_id', $this->getRequest()->getParam('id'));

This is assuming you have created a collection resource model for your Messages entity.

NB: please try to avoid using the Object Manager directly

Instead you can inject the collection class in your constructor:

protected $_messagesCollection;

public function __construct(
    ...
    \Custom\Module\Model\ResourceModel\Messages\Collection $messagesCollection,
    ...)
{
    ...
    $this->_messagesCollection = $messagesCollection;
}

And then you can use your variable directly in your code:

$messages = $this->_messagesCollection->addFieldToFilter('posts_id', $this->getRequest()->getParam('id'));