Below steps was help to fix for ssh rsa-key login with user admin (in my case it work well even with StrictModes in sshd conf). The reason is that the users home folder ~/ is not allowed to be writable to group and other, so let’s try to “chmod 755 /volume1/homes/user: should do the trick.
Step 1. Check if your pubkey is ok: it’s strange but sometimes during copy/paste something happens and it’s not working:
ssh-keygen -l -f /var/services/homes/admin/.ssh/authorized_keys
Step 2.
chmod 755 /var/services/homes/admin
Step 3.
chown admin:users /var/services/homes/admin/.ssh
chmod 700 /var/services/homes/admin/.ssh
Step 4.
chown admin:users /var/services/homes/admin/.ssh/authorized_keys
chmod 644 /var/services/homes/admin/.ssh/authorized_keys
Source: https://forum.synology.com/enu/viewtopic.php?f=90&t=116726&p=441504
