Dear Hasnain
As you already have limited legal leave to remain in the UK it may be in you and your family best interests to continue/extend your leave in the UK. The reason for this being is that if you are eligible to switch to a Tier 2 visa you may do so, in doing this your dependants will also have legal leave. Applying for further limited leave to remain whilst still on a visa means that provided you can demonstrate you meet the criteria for that visa you are entitled to be granted further leave and so would your family as your dependants.
As your child requires medical care this may be given despite you having limited leave depending on how long you and your family have been residing in the UK whilst having limited leave. Therefore, as you currently on a Post-Study worker visa and or may be able to switch to a Tier 2, provided that you have resided in the UK continuously for a minimum of 1 year your child may be entitled to some limited services provided by the NHS for free.
Services provided for free by the NHS for those with limited leave are as follows:
- Registration with a GP (at the discretion)
- Free treatment from GP (once registered)
- Treatment given in an accident and emergency (A&E) department or in an NHS walk-in centre that provides services similar to those of an A&E department;
- Treatment for certain infectious diseases (but for HIV/AIDS, only the first diagnosis and counselling that follows it are free);
- Compulsory psychiatric treatment; and
- Family planning services
However, as stated above if you have lived in the UK legally for at least 12 months then you and your child may be able to receive the full range of hospital treatment provided under the NHS.
Alternatively if you find that that you cannot extend your further leave and cannot switch to a Tier 2 then your other option is to make an application for your son for Discretionary leave arguing Article 8 (right to enjoy private and family life) and Article 3 (on the basis of medical grounds) whilst he still has valid leave to remain in the UK as your dependant.
However, with a discretionary leave application there is no certainty as there is no legal criteria to satisfy therefore each case is decided on a case by case basis. Therefore you case must be exceptional and clearly have compelling and compassionate grounds. Similar applications where medical grounds have been argued will succeed where the Applicant can clearly show that the treatment and medication required is not available in their home country and that without the treatment/medication their lives would be seriously hindered or life threatening. As the Home Office will be exercising their own policy they do not have to grant a foreign national further leave on this basis as there is nothing in law which states they must, this application is at the Home Offices discretion.
For further legal advice on this matter with regards to all your options, and the implications of each application you should approach a firm of accredited immigration solicitors for a full consultation.
Regards
Greenfields Solicitors
www.greenfieldssolictors.com 
