add a variable to your trigger api call as shown here:

https://docs.gitlab.com/ee/ci/triggers/#making-use-of-trigger-variables

then use the only prperty inside your gitlab.yml file as shown here :

https://docs.gitlab.com/ee/ci/variables/#environment-variables-expressions

then only if the variable exists the job will be execute

for example

job1:
  script: echo "HELLO"
  only:
    variables:
      - $variables[API_CALL]=true

Probably changes in GitLab makes answers above not working. The

only:
  variables:
    - $variables[....]

syntax trigger CI Lint.

For others that come here like me, here's how I trigger a specific job:

job1:
  script: 
    - echo "HELLO for job1"
    - "curl 
      --request POST
      --form token=$CI_JOB_TOKEN
      --form ref=master
      --form variables[TRIGGER_JOB]=job2
      https://gitlab.com/api/v4/projects/${CI_PROJECT_ID}/trigger/pipeline"
  except:
    - pipelines

job2:
  script: echo "HELLO for job2"
  only:
    variables:
      - $TRIGGER_JOB == "job2"

⚠️ Note the except - pipelines in job1, else, you go in infinite Child pipeline loop!

By using variables you can do:

Use this curl command to trigger the pipeline with a variable

curl --request POST --form token=${TOKEN} --form ref=master --form "variables[TRIGERRED_JOB]=job1" "https://gitlab.com/api/v4/projects/${CI_PROJECT_ID}/trigger/pipeline"

Ofcourse you have to set the variable accordingly.

Define your jobs with the appropriate variable:

job1:
  script: echo "HELLO for job1"
  only:
    variables:
      - $variables[TRIGERRED_JOB] == "JOB1"

job2:
  script: echo "HELLO for job2"
  only:
    variables:
      - $variables[TRIGERRED_JOB] == "JOB2"

if you are running the curl from inside another/same job you can use ${CI_JOB_TOKEN} instead of $TOKEN and

https://docs.gitlab.com/ee/ci/triggers/#making-use-of-trigger-variables