From the API, there are several ways to get filtered data.

To do this you need to use getTableValues, and add the filtered rows parameter, also called

filterRowIds.

Use data from an existing filtered view : applyViewFilters

In filtered rows, enter the filter ID as follows:

{"applyViewFilters":12345}

It can be found in the XHR console as view_id :

Filtering directly via the query : filterGroup

In filtered rows, enter the filter ID as follows:

In this example, I want to display all rows in my table that have the text "hello" in the column with field_Id 320862.

Other examples available in documentation :

Filters list