{
    "statusCode": <HTTP код ответа>,
    "headers": <словарь со строковыми значениями HTTP-заголовков>,
    "multiValueHeaders": <словарь со списками значений HTTP-заголовков>,
    "body": "<содержимое ответа>",
    "isBase64Encoded": <true или false>
}

mkdir sample-app && cd sample-app
npm init -y
npm install express
touch index.js

const express = require('express');
const app = express();
app.use(express.urlencoded({ extended: true }));
app.use(express.json());
app.get('/api/info', (req, res) => {
    res.send({ application: 'sample-app', version: '1.0' });
});
app.post('/api/v1/getback', (req, res) => {
    res.send({ ...req.body });
});
app.listen(3000, () => console.log(`Listening on: 3000`));

$ curl 'http://localhost:3000/api/info'
{"application":"sample-app","version":"1"}

npm i --save serverless-http

const express = require('express');
const app = express();
const serverless = require('serverless-http');
app.use(express.urlencoded({ extended: true }));
app.use(express.json());
app.get('/api/info', (req, res) => {
    res.send({ application: 'sample-app', version: '1.0' });
});
app.post('/api/v1/getback', (req, res) => {
    res.send({ ...req.body });
});
//app.listen(3000, () => console.log(`Listening on: 3000`));
module.exports.handler = serverless(app);

npm i -g serverless serverless-yandex-cloud

service: sample-app
frameworkVersion: ">=1.1.0"
configValidationMode: off
provider:
  name: yandex-cloud
  runtime: nodejs12-preview
plugins:
  - serverless-yandex-cloud
package:
  exclude:
    - ./**
  include:
    - ./package.json
    - ./**/*.js
functions:
  express:
    # this is formatted as <FILENAME>.<HANDLER>
    handler: index.handler
    memory: 128
    timeout: 5

serverless deploy 

$ curl 'https://functions.yandexcloud.net/%function-id%/api/info'
{"errorCode":400,"errorMessage":"Invalid functionID: /%function-id%/api/info",
"errorType":"ProxyIntegrationError"}

openapi: 3.0.0
info:
  title: Sample API
  version: 1.0.0
paths:
  /api/info:
    get:
      responses:
        '200':
          description: Ok
      x-yc-apigateway-integration:
        type: cloud_functions
        function_id: %function_id%
        tag: $latest
        service_account_id: %service_account_id%
  /api/v1/getback:
    post:
      responses:
        '200':
          description: Ok
          content:
            application/json:
              schema:
                $ref: '#/components/schemas/Test'
      requestBody:
        required: false
        content:
          application/json:
            schema:
              $ref: '#/components/schemas/Test'
      x-yc-apigateway-integration:
        type: cloud_functions
        function_id: %function_id%
        tag: $latest
        service_account_id: %service_account_id%
components:
  schemas:
    Test:
      type: object

$ curl 'https://%api-gw-id%.apigw.yandexcloud.net/api/info'
{"application":"sample-app","version":"1"}

paths:
  /api/{proxy+}:
    get:
      x-yc-apigateway-integration:
        type: cloud_functions
        function_id: d4e***
        tag: $latest
        service_account_id: aje***
      responses:
        200:
          description: Ok
      parameters:
        - explode: true
          in: path
          name: proxy
          required: true
          schema:
            type: string
          style: simple

const express = require('express');
const serverless = require('serverless-http');
const app = express();
app.use(express.urlencoded({ extended: true }));
app.use(express.json());
app.get('/api/info', (req, res) => {
    res.send({ application: 'sample-app', version: '1.0' });
});
app.get('/api/pet/:name?', (req, res) => {
    res.send({ ...req.params });
});
module.exports.handler = (event, context) => {
    const patchedEvent = {
        ...event,
        path: event.url,
        originalPath: event.path,
    }
    return serverless(app)(patchedEvent, context);
}