public void sendMessage(final Long subscriptionId, final JsonRpcResult msg) {
    final Subscription subscription = subscriptions.get(subscriptionId);

    if (subscription != null) {
      final SubscriptionResponse response = new SubscriptionResponse(subscription, msg);
      vertx.eventBus().send(subscription.getConnectionId(), Json.encode(response));
    }
  }
The SubscriptionManager is responsible for managing subscriptions and sending messages to the
clients that have an active subscription.
ethereum/api/src/main/java/org/hyperledger/besu/ethereum/api/jsonrpc/websocket/subscription/SubscriptionManager.java