I have connection to a remote server in FileZilla. So far I am able to download massively every file of the directory, but is huge and contains much other files than needed.
How can I download the files that comply with the condition "begin with..."?
You can setup a Directory listing filter (in View menu).
The filter is followed even during transfers.
A slight disadvantage is, that the filter is a permanent setting. So you have to go back after the transfer and unset it. The filter is also relatively complex to setup.
If you prefer a temporary-style filter for transfers, you probably have to use another client.
For example with WinSCP, the filter is part of transfer settings. In WinSCP (while permanent presets are also possible), you can setup an ad-hoc settings (including a filter) for each transfer.
(I'm the author of WinSCP)