The default configuration for ton full node (https://github.com/ton-blockchain/ton/blob/master/validator/validator.h#L95) is to save state for 1 hour. Block related data is saved for 1 week. Both are moved to archive dir after this period. Archive dir is deleted after 1 year. This configuration can be changed and archive nodes for example will deploy their nodes with much bigger values so users can query state at anytime in history.
In order to query an old state (more than 1 hour ago) you will need to use an archive node. Using the TON APIv4, you can query GET /block/<seqno>/<address>/run/<method>/<args?> which can be used with method=get_wallet_data to query jetton balance.
In Toncenter for example, it is not possible to query a method from old states. However, you can use getTransactions with archival=true to get all transactions and calculate the exact amount on each state.
Transactions in non archive (default) nodes will be stored for 1 week.
Use TON API https://tonapi.io/docs
And API Uniton - https://api.uniton.app/
Can you add an example of using these APIs to the answer? What API method and how to use it
Stackoverflow rules normally don't encourage answers that just send to an external link since external links can break. Better to copy paste a relevant part of the link content into your answer. Also better for this answer SEO. Can you please add a short example of the relevant API call?
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