Hello!

I suppose you may use silent_mode option to prevent sending push notifications.

1) In file modules/boonex/classes/BxMessngerModule.php find the method:

public function sendNotifications($iLotId, $iJotId, $aOnlineUsers = [], $aRecipients = [], $sType = BX_MSG_NTFS_MESSAGE)

and replace code:

bx_alert($sModule, !$bIsMention ? 'got_jot_ntfs' : 'got_mention_ntfs', $iLotId, $this->_iProfileId, array(
    'object_author_id' => $iPart,
    'recipient_id' => $iPart,
    'subobject_id' => $iJotId
));

with this code:

bx_alert($sModule, !$bIsMention ? 'got_jot_ntfs' : 'got_mention_ntfs', $iLotId, $this->_iProfileId, array(
    'object_author_id' => $iPart,
    'recipient_id' => $iPart,
    'subobject_id' => $iJotId,
    'silent_mode' => BX_NTFS_SLTMODE_SITE_PUSH
));