At the end of the season you need to have 14 signed players. That is the minimum number. Please note that an unassigned player in your team is not part of your Squad.
If you do not have 14 players, the system in Top Football Manager adds some weaker players until you reach the minimum.
That's the reason why you see new players in your team at the beginning of the season and if you do not like them you can simply dismiss them at any time as long as you have the minimum number of players in your Squad.
Additional note: The maximum number of players that you can have is 25.