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В конфигах консоль и веб:
'log' => [
    'traceLevel' => YII_DEBUG ? 3 : 0,
    'targets' => [
        [
            'class' => 'yii\log\FileTarget',
            'levels' => ['info'],
            'categories' => ['test_category'],
            'logFile' => '@app/runtime/logs/test_success.log',
        ],
        [
            'class' => 'yii\log\FileTarget',
            'levels' => ['error'],
            'categories' => ['test_category'],
            'logFile' => '@app/runtime/logs/test_error.log',
        ],
    ],
],

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В коде:
Yii::error('error message', 'test_category');
Yii::info('success message', 'test_category');