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How to add a custom field depends on back order option in product edit page(under advance inventory) in magento 2 admin

Try following way:

app/code/SR/MagentoCommunity/view/adminhtml/ui_component/product_form.xml

<?xml version="1.0" encoding="UTF-8"?>
<form xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Ui:etc/ui_configuration.xsd">
 <modal name="advanced_inventory_modal">
 <fieldset name="stock_data">
 <container name="container_backorders">
 <field name="backorders" formElement="select" component="SR_MagentoCommunity/js/backorders"/>
 <field name="custom_input" formElement="input">
 <settings>
 <scopeLabel>[GLOBAL]</scopeLabel>
 <label translate="true">Custom Input</label>
 <dataScope>custom_input</dataScope>
 </settings>
 </field>
 </container>
 </fieldset>
 </modal>
</form>

app/code/SR/MagentoCommunity/view/adminhtml/web/js/backorders.js

define([
 'underscore',
 'uiRegistry',
 'Magento_Ui/js/form/element/select'
], function (_, uiRegistry, select) 
 'use strict';

 return select.extend(

 initialize: function () 
 this._super();
 var customInput = uiRegistry.get('index = custom_input');
 if (this.value() == 1) 
 customInput.show();
 else 
 customInput.hide();
 
 return this;
 ,
 /**
 * On value change handler.
 *
 * @param String value
 */
 onUpdate: function (value) 
 var customInput = uiRegistry.get('index = custom_input');
 if (value == 1) 
 customInput.show();
 else 
 customInput.hide();
 
 return this._super();
 
 );
);

Now this new field will visible if you select Allow Qty Below 0 from backorder dropdown.

[Update]

You need to change xml for M2.1

app/code/SR/MagentoCommunity/view/adminhtml/ui_component/product_form.xml

<?xml version="1.0" encoding="UTF-8"?>
<form xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Ui:etc/ui_configuration.xsd">
 <modal name="advanced_inventory_modal">
 <fieldset name="stock_data">
 <container name="container_backorders">
 <field name="backorders">
 <argument name="data" xsi:type="array">
 <item name="config" xsi:type="array">
 <item name="component" xsi:type="string">SR_MagentoCommunity/js/backorders</item>
 </item>
 </argument>
 </field>
 </container>
 <field name="custom_input">
 <argument name="data" xsi:type="array">
 <item name="config" xsi:type="array">
 <item name="dataType" xsi:type="string">number</item>
 <item name="formElement" xsi:type="string">input</item>
 <item name="visible" xsi:type="boolean">true</item>
 <item name="label" xsi:type="string" translate="true">Custom Input</item>
 <item name="dataScope" xsi:type="string">custom_input</item>
 </item>
 </argument>
 </field>
 </fieldset>
 </modal>
</form>