How to call widget with products of specific category in ".phtml" file?

There is a widget for arbitrary product lists (as mentioned by @Nits). If you insert the widget on any CMS page or block and turn off the WYSIWYG editor ("Hide editor" button), you can see how the parameters look like.

For example, I created the widget with the condition "category = 4", showing five products:

{{widget type="Magento\CatalogWidget\Block\Product\ProductsList" title="My products" products_count="5" template="product/widget/content/grid.phtml" conditions_encoded="a:2:[i:1;a:4:[s:4:`type`;s:50:`Magento|CatalogWidget|Model|Rule|Condition|Combine`;s:10:`aggregator`;s:3:`all`;s:5:`value`;s:1:`1`;s:9:`new_child`;s:0:``;]s:4:`1--1`;a:4:[s:4:`type`;s:50:`Magento|CatalogWidget|Model|Rule|Condition|Product`;s:9:`attribute`;s:12:`category_ids`;s:8:`operator`;s:2:`==`;s:5:`value`;s:1:`4`;]]"}}

From that you can see that the class is Magento\CatalogWidget\Block\Product\ProductsList and you can create it programmatically as follows:

$productsBlock = $this->getLayout()->createBlock(\Magento\CatalogWidget\Block\Product\ProductsList::class);
$productsBlock->setTitle("My products");

But "conditions_encoded" is a serialized array (with some characters replaced for WYSIWYG compatibility). This serialized array is difficult to construct manually, but luckily you can also use "conditions" with the unserialized value instead in PHP code. So you can replace the last line from above with:

        1 => [
            'type' => \Magento\CatalogWidget\Model\Rule\Condition\Combine::class,
            'aggregator' => 'all',
            'value' => '1',
            'new_child' => '',
        '1-1' => [
            'type' => \Magento\CatalogWidget\Model\Rule\Condition\Product::class,
            'attribute' => 'category_ids',
            'operator' => '==',
            'value' => '4',

Then output:

echo $productsBlock->toHtml();

You can do it via static-block: 1) add static block with widget of catalog product list and add category id in widget condition. (content menu >> Blocks >> add new >> click on show/hid button >> insert widget >> select catalog product list from widget type >> add title >> select category in condition field (click on + icon) >> insert widget >> save this block. 2) you can call this block in phtml file as well as xml file.

<?php echo $block->getLayout()->createBlock('Magento\Cms\Block\Block')->setBlockId('block_identifier')->toHtml();?>


<block class="Magento\Cms\Block\Block" name="Promo">
        <argument name="block_id" xsi:type="string">promo</argument>

I Hope this will help you.