Yes, there’s several things that might help you.
First of all, I guess you might want to simulate an E-Mail for simplicity reasons, so you to tell Zamamd that this is actually an E-Mail. Also, phone notes (which will be the default when creation happens) will always be from the agent. If you set the customer correct, that should be good to go normally.
Anyway, here’s an API example for the screenshot below, this will exactly create what you see on the screen. So you can fiddle around with that to meet your requirenment. I hope this helps. 
{
"group_id": 1,
"priority_id": 3,
"state_id": 2,
"organization_id": 2,
"title": "Some API-Test",
"owner_id": 3,
"customer_id": 6,
"note": null,
"first_response_at": null,
"first_response_escalation_at": "2019-01-31T10:50:28.000Z",
"first_response_in_min": null,
"first_response_diff_in_min": null,
"close_at": null,
"close_escalation_at": "2019-02-06T10:50:28.000Z",
"close_in_min": null,
"close_diff_in_min": null,
"update_escalation_at": "2019-02-01T11:20:28.000Z",
"update_in_min": null,
"update_diff_in_min": null,
"last_contact_at": "2019-01-14T15:50:28.000Z",
"last_contact_agent_at": null,
"last_contact_customer_at": "2019-01-14T15:50:28.000Z",
"last_owner_update_at": null,
"create_article_type_id": 5,
"create_article_sender_id": 2,
"article_count": 1,
"escalation_at": "2019-01-31T10:50:28.000Z",
"pending_time": null,
"type": "email",
"time_unit": null,
"preferences": {
"escalation_calculation": {
"first_response_at": null,
"last_update_at": "2019-01-14T15:50:28.000Z",
"close_at": null,
"sla_id": 1,
"sla_updated_at": "2019-01-15T08:30:55.830Z",
"calendar_id": 1,
"calendar_updated_at": "2019-01-17T10:53:45.906Z",
"escalation_disabled": false
}
},
"updated_by_id": 3,
"created_by_id": 3,
"created_at": "2019-01-14T15:50:28.000Z",
"updated_at": "2019-01-18T17:49:29.928Z",
"tags": "gets,ignored,anyway,noreply",
"article": {
"type_id": 1,
"sender_id": 2,
"from": "LeTest <alias@secret.tld>",
"to": "Users",
"cc": null,
"subject": null,
"reply_to": null,
"message_id": null,
"message_id_md5": null,
"in_reply_to": null,
"content_type": "text/html",
"references": null,
"body": "Some amazing test!",
"internal": false,
"preferences": {},
"updated_by_id": 3,
"created_by_id": 3,
"origin_by_id": 5,
"created_at": "2019-01-14T15:51:50.000Z",
"updated_at": "2019-01-14T15:51:50.341Z",
"attachments": [],
"type": "email",
"sender": "Customer",
"created_by": "alias@secret.tld",
"updated_by": "alias@secret.tld",
"origin_by": "test2@test.com"
}
}
Of course you can leave out not needed stuff. 