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I'm using the pgr_astar function of Postgres and I want to personalize the optimal path proposed according to the preferences of the user. For example if the pg_astar propose the red path, I want to make this function propose the orange path if I specify that the user wants to go through the blue point.

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If you know, that the route should go through the blue point, then you could use pgr_dijkstraVia: https://docs.pgrouting.org/latest/en/pgr_dijkstraVia.html#pgr-dijkstravia

SELECT * FROM pgr_dijkstraVia(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id',
    ARRAY[1, 2, 3]
);

Where 1, 2 and 3 are your vertex ID's and "2" is the blue point.

This is function uses Dijkstra and not A-Star, but I'm not aware of a strong reason not to use Dijkstra.

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