Monal is a modern Jabber/XMPP client for iOS and Mac OS that works well with most XMPP servers. Get it here:
Siskin is another Jabber/XMPP client for iOS. It supports audio and video calls. Get it here:
Movim is a web-client that works well in the Safari mobile browser. It can be installed as a PWA app by visiting a Movim instance and selecting the "Add to home screen" option from the menu of your browser. Push notifications can be enabled in the Movim settings and will be delivered through the browser's web-push feature.