SQL Query: how to select records, but if a parent record exists select the most recent child of it - sql

Question

I have a complicated query I need to figure out but I'm not well versed enough in writing queries and sub queries.
The problem: I need to retrieve unique Patient records but if a record has a non null master_patient_id, I need to subquery or join on that master_patient table and query for the most recent (created_at desc limit 1) child patient of that master_patient.
The reason for this is that our system will create a new patient record for the same patient if they were readmitted to the same facility. Upon creating the 2nd record for a given patient we also create a master_patient record to associate the 2 patient records with it so that the system can know they are the same patient.
Now, I need to show a list of non duplicate patients. So I need to have a query that will get patients from the patient record, but query the master_patient table and only retrieve the latest patient associated to its master_patient.
Patient Table has: id, name, master_patient_id
and the patient belongs_to master_patient but isn't required to be present.
Master Patient table just has an id and has_many patients.
Desired results: should be unique patient records, but the only way to find out if patients are unique among themselves is to query the master_patient table to see if any patients belong_to it and then just retrieve the latest patient (child of master_patient).
I can't base my query off master_patient because those don't exist for patients that only have 1 record. Should I use some type of join or subquery?
Update: Thanks to #τεκ I was able to tweak his query to work in Postgres:
Update 2: 1 more tiny tweak to the query to make it shorter and correct a null id being returned:
SELECT MAX(patients.id) as id, *
FROM "patients"
JOIN (
SELECT MAX(created_at) AS created_at,
patient_master_id,
COALESCE(patient_master_id, id) pm_id
FROM patients
GROUP BY patient_master_id,
COALESCE(patient_master_id, id)
) s
ON (s.pm_id = patients.id or s.patient_master_id = patients.patient_master_id)
AND s.created_at = patients.created_at
GROUP BY patients.id, s.created_at, s.patient_master_id, s.pm_id

Answer 1

select max(id) as id from patient p
join (select
max(created_at) as created_at,
master_patient_id,
case when master_patient_id is null then id else null end as id
from patient
group by master_patient_id, case when master_patient_id is null then id else null end
) s on (s.id = p.id or s.master_patient_id = p.master_patient_id) and s.created_at = p.created_at
There's probably a simpler, postgres-specific way to do it, but I don't know postgres. In T-SQL it's cross apply.