Very few banks, especially outside of EU/EEA, are going to be interested in you for that little money. Even 10x that amount isn't interesting enough. And as
@Gediminas mentions, even if you do manage to open an account, the costs are going to eat up your balance quickly.
Most Swiss banks require 250,000 CHF/EUR minimum, usually 500,000 – 1 million CHF/EUR. There are only five exceptions I can think of:
- CIM Banque: minimum 5,000 CHF/EUR required, IIRC.
- Postfinance: sometimes opens accounts for Italians if you contact them or visit in person (maybe not right now though due to coronavirus), low minimums/fees.
- Dukascopy: can be opened online with their app, no minimum required.
- Swissquote: only good for transfers to/from your own accounts, they don't like third-party transactions, no fixed fees or minimums.
- Strateo: same deal as Swissquote.
If you are content with EU, you can try Bitwala (using solarisBank's license), N26, and Bunq. Keep an eye on Revolut. They are beginning to transition EU customers over to Lithuania, first the EMI and then eventually to their special banking license.