The way the story is told is extremely bad. I feel bad that you are completely lost too.
Basically, at the beginning of episode 4, the moment the 'Another Ex-Aid' was defeated, this allowed for the real (2018) Ex-Aid to regain his memory and transform again. But after the 'Another Ex-Aid' was revived, Ex-Aid loses his power and his memory as a Kamen Rider as well.
In this 2018 timeline, Ex-Aid is a doctor that is seeking the boy's father to understand that what the son really needs most is his father. They then find out that for the past 2 years, 'Another Ex-Aid' has been searching for compatible organ donors through the game.
However, Brave explained that if he had met the boy 6 months earlier, he could have done a successful surgery. (This wouldn't be an issue since Zi-O will be going 2 years back to then introduce the boy to Brave thus solving the boy's crisis later on.)
2018 Ex-Aid then hands the watch that was given to him in the past which can be seen towards the end of the episode in the year 2016 to Zi-O in the current year of 2018.
While all this was happening, Geiz was back in the past (2016) talking to the old Brave and Ex-Aid who were still fighting Bugsters back then.
Just like episode 3, that was when the Time Jacker created the 'Another Ex-Aid'.
Zi-O travels back in time to the year 2016 where Geiz and the 2016 Ex-Aid was fighting the 'Another Ex-Aid' . Fighting ensues but slowly, Ex-Aid was losing his powers.
Zi-O finds out the secret to defeating the 'Another Ex-Aid' is by having the same Ex-Aid fight it. Thus, he takes on the role of Ex-Aid through Armor Time.
Another Ex-Aid was defeated but the damage was done like in Build. Ex-Aid is no longer a Kamen Rider. But in order for Zi-O to get the Ex-Aid watch to begin with, Zi-O hands Ex-Aid an empty watch which will in the current timeline of 2018, pass him that watch with the Ex-Aid armor.
In both Build and Ex-Aid's story, the 2018 versions of them do not have their memories until for a split second that they gain their memories back and hands over the watch. Or when the 'Another' version of them is defeated momentarily until they are revived by the Time Jacker that is managing them to be the next Time Overlord.
By the end of the episode, we can see that in 2018, the son was cured thanks to Brave's surgery and the father and son are both leading a happy life.