Able to see live traffic stats on GUI , but not through REST API

GET /mgmt/tm/sys/connection should yield the "tmsh show sys conncetion" output. For example,

$ curl -sku admin:admin https://192.168.184.50/mgmt/tm/sys/connection | jq .
{
  "kind": "tm:sys:connection:connectionstats",
  "selfLink": "https://localhost/mgmt/tm/sys/connection?ver=15.1.2",
  "entries": {
    "https://localhost/mgmt/tm/sys/connection/0": {
      "nestedStats": {
        "entries": {
          "connectionId": {
            "value": 0
          },
...

Since the call may generate a large amount of data (iControl REST does not prompt you Y/N, so be careful), it is prudent to add a filter. Add the options query string to the endpoint. Separate the parameters with comma (,): e.g,

$ curl -sku admin:admin https://192.168.184.50/mgmt/tm/sys/connection?options=cs-server-addr,10.200.20.10 

If you have more than one filters, continue with the commas: e.g,

$ curl -sku admin:admin https://192.168.184.50/mgmt/tm/sys/connection?options=cs-server-addr,10.200.20.10,cs-server-port,8

For more information on query strings, refer to the "About Query Parameters" section of iControl REST API User Guide. You can download the PDF from iControl REST Home.